1. Character
First off you have to look at the most crucial aspect of a character… their character.
Zoro’s character can genuinely be said to be almost entirely about strength. Getting stronger and stronger, until he’s so strong his name echoes in the heavens, is quite literally the driving force of his entire life. The majority of his character revolves around this, strength and fighting, with what remains revolving around pride (in strength) and honor. It’s emphasized in his rigorous training and in his toughness, which has been called the highest out of the entire crew, meaning higher than Luffy’s.
Sanji’s character largely revolves around women and cooking. His dream is to find the All Blue and his profession is to cook. He is a naturally talented combatant and has been living with fighting, including high quality training, as a major part of his life since he was a kid. This has developed his great leg strength and skill and heightened his combat instincts. His character itself, however, is not very much about strength. For Sanji, strength is secondary despite his incredible talent and familiarity with it.
Conclusion on character: Zoro’s character emphasizes strength much more heavily than Sanji’s. Nearly all of his character revolves around it. It even revolves around it more than Luffy’s, up until Enies Lobby where Luffy started focusing more on it.
2. Roles in the story
What a character’s basic role in the story is, is hugely important for how strong they are. Important antagonists are usually strong, main protagonists are nearly always strong. People at the top of the world, in a Shonen, are nearly always strong, etc.
Zoro’s role in the story is to be somewhat of a secondary protagonist within the main cast. He has been called one of the 3 “cores” of the story by the author and was the second major character introduced after only the main character. He has more panel time than other main characters, especially in some arcs like Skypiea and Whiskey Peak. His drive in which we follow him, as detailed above, is that of constantly becoming stronger and stronger. Within the crew, Zoro’s formal role is exclusively focused on his strength in combat. There is nothing else to him. Informally he also fills many of the roles of a first mate, which in OP is generally held by the second strongest character. Due to his strength and confidence he is implicitly Luffy’s right hand man in terms of leadership and direction of the crew. As the second strongest fighter in the crew, he has the highest responsibility after only Luffy to bear the heaviest burdens and take on the strongest fighters when Luffy can’t, a point especially illustrated by his actions during the climax sequence of Thriller Bark.
Sanji’s formal role in the story is to be the chef and, slightly less formally, the third strongest fighter in the crew. He derives his great strength from talent and childhood training as detailed above but not from rigorous training. We don’t generally follow him in a quest to grow stronger. He fights powerful enemies and overcomes them but growing stronger is not a major theme for him. Informally he is also somewhat of a covert operative/tactician of the crew, being intelligent and highly perceptive. Due to his strength and confidence he is implicitly Luffy’s left hand man in terms of leadership and direction of the crew. If both Luffy and Zoro are gone, the responsibility of bearing the heaviest burdens in terms of strength and leadership fall to Sanji, a point illustrated by his actions as acting commander of the Straw Hat pirates’ ship during the absence of both Luffy and Zoro.
Conclusion on role in the story: Zoro’s role focuses much more heavily on strength than Sanji’s. Sanji’s intelligence and cooking are significant aspects of his character and the only thing Zoro has that’s comparable is his sometimes acting like a first mate.
3. Actions in the story
This is just about clear cut actions. No portrayal/subtext.
Zoro doesn’t do much else in the story except fighting and training. When on the ship he either trains or rests. Within arcs he fights enemies. Outside of Luffy he fights both the most and the strongest enemies of anyone in the crew. Virtually as much emphasis is given to his growth and him increasing his abilities as to Luffy and more than anyone else. Up until Enies Lobby he had gained more power-ups than anyone else in the crew.
Sanji fights enemies frequently but also uses his intelligence to support the crew. On the ship he cooks and hits on the girls of the crew. Within arcs he is generally a mixture of an infiltrator and fighter, leaning more toward the latter. Among the crew he is given a fair amount of emphasis on strength and growth, but less than Zoro. He hadn’t gained a power-up until Enies Lobby, where he got one, but no more up until the timeskip.
Conclusion on actions in the story: Zoro does more things that should logically raise his strength than Sanji does. He trains more, fights stronger enemies and fights more enemies. This is reinforced by how more emphasis is given to his growth and overcoming enemies.
4. Portrayal in the story/implied subtext
– Zoro joined the crew by being blackmailed by Luffy. Out of the entire crew he is the only one who didn’t willingly become a subordinate of Luffy’s after being impressed by him. Upon joining, he told Luffy he would kill him if he ever made him go against his dream. This paints a picture that is not much like a willing subordinate, but a man joining out of pure survival necessity while reinforcing he’ll split ways and become hostile if need be.
– Sanji joined the crew after being impressed by Luffy and accepting becoming his subordinate to go into the Grand Line where the object of his own dream lied. During his introductory arc he was seen to be astonished at Luffy and Zoro’s drive and the relentless way they followed their dreams. Sanji willingly becomes Luffy’s subordinate and though he’s very strong, their relationship is never really more than that.
– Zoro has a relationship with his captain built on a complete mutual trust in terms of strength. Both view the other’s strength in an extremely high regard. During Whiskey Peak each directly admits they don’t know who is stronger between them. During Little Garden each identically scoffs at the notion of the other having been defeated. During Skypiea Luffy is astonished that anyone could have defeated Zoro. During Water Seven, each wordlessly trusts in the other’s strength to perform an equally strong move to break through the Aqua Laguna wave. During Thriller Bark Zoro is able to stay conscious while enduring pain that KO’d Luffy on top of his own to save Luffy. As such Luffy and Zoro’s relationship is conveyed in a sometimes less explicit, but powerfully understated way, with huge underlying significance to the above mentioned scenes. At the onset of the timeskip Zoro reinforces his conviction to support Luffy with his strength. Other than the ones mentioned, there are lots of scenes reinforcing the dynamic of the closeness of their strength throughout the story.
– Zoro has a relationship with Sanji built on an eternal rivalry due to both being forceful personality types that don’t admit weakness to anyone, and coming off on a slightly bad note. He respects him as a rival and has been seen to be content at Sanji’s strength. Sanji also respects Zoro and trusts his strength. Their rivalry is often played for comedy and for cool but shallow scenes, but it can be gleaned that it has a significant underlying depth as well such as when Sanji is as willing as Zoro to take Luffy’s pain at Thriller Bark after they are the only ones that were able to get up after Kuma’s Ursus Shock attack. There are lots of scenes reinforcing this dynamic throughout the series, both the closeness of their strengths and their refusal to admit any sort of inferiority to the other.
– Sanji’s relationship with Luffy is that he trusts him fully as his captain and wishes to support him, with his cooking as well as his strength. They often fight together, alongside Zoro, as the so-called monster trio of the crew. There are numerous scenes reinforcing the closeness of Sanji’s strength to Luffy’s throughout the series, mostly through the portrayal of Luffy, Zoro and Sanji as the three top crewmembers.
– Zoro and Sanji also have a mutual relationship with Luffy where they act as his right and left hand men. This has been mentioned before but deserves a point of its own. Whenever Luffy fights a boss Zoro and Sanji usually fight some of their strongest subordinates. Zoro and Sanji are portrayed as the two monsters whilst Luffy is away. They each back up Luffy even though they can take charge personally if needed. There are numerous scenes showcasing this dynamic throughout the series, after and before the timeskip.
– During the Sabaody archipelago arc, Zoro alongside Luffy was made into one of the “11 Supernovas”, notable rookie pirates with bounties over 100 million. This decision served to set him apart from Sanji and set him together with Luffy, following Thriller Bark.
– When the timeskip happened, Zoro was directly trained by one of the strongest men in the world, “Hawkeyes” Mihawk. The only other person to be directly trained by one of the strongest men in the world, Silvers Rayleigh, was Luffy. Sanji’s training involved self-teaching himself new techniques as he fought strong enemies as well as learning new cooking techniques. This clearly unites Luffy and Zoro while setting them apart from Sanji to a moderate degree. When Sanji returned after the timeskip one of the first things he had to say was that Luffy must have become outrageously strong after training with Rayleigh. Zoro was trained by a top tier just like Luffy. Consequently, the same thing, that Sanji must believe he has become outrageously strong, logically applies to Zoro. This again serves to set Luffy and Zoro apart from Sanji in the strength they attained over the timeskip.
– As the timeskip has proceeded, Zoro stands virtually untouched 180 chapters in. He has crushed an enemy that Luffy called strong and another that made Luffy struggle. One of Doflamingo’s strongest subordinates barely made him break a sweat and he was able to fend off an attack from an Admiral and was called ferocious by him. Sanji has struggled with numerous opponents although they were very powerful ones. He was called strong by Doflamingo albeit the latter defeated him with a technique no one knows how to counter. All in all, the dynamic shown is that the M3 are all on a similar level but Zoro stands out especially for barely even being touched and even briefly countering an Admiral. Few fans have failed to notice the immaculate portrayal of Zoro and he has yet to be pushed hard. In Fishman Island, Zoro was given a fishman opponent who had gone through the same exact power-up procedure as Luffy’s. He was thus set apart together with Luffy.
Conclusion on portrayal: Luffy/Zoro and Zoro/Sanji are both strong, emphasized relationships that exist in the story as far as strength is concerned. It’s clear from this that Zoro is close to Luffy and Sanji is close to Zoro. Due to the portrayal as a trio it’s also clear that Sanji is relatively close to Luffy. The Luffy/Zoro scene however outweigh the Zoro/Sanji scenes when viewed holistically and with respect to their underlying significance. Luffy/Zoro scenes are usually done with more subtext and in more significant moments as opposed to Zoro/Sanji often being more comedic and stylistic. In Zoro/Sanji’s case the fact that they have a rivalry is a big part of their mutual portrayal. In Luffy/Zoro the portrayal is just about strength as that is what links them together and always has. In some scenes both relationships are emphasized, but Luffy/Zoro is emphasized more. Luffy and Zoro are the only ones that have ever fought each other outright and been depicted as equally matched. Luffy has outright admitted he doesn’t know if he’s stronger than Zoro at a time. Viewed across the entire series, Zoro and Luffy’s personal relationship, which barely resembles a boss/subordinate relationship at all nor did it start out as one, has the most underlying depth and significance between the two relationships.
5. The stance of official materials
The databooks are approved by Eiichiro Oda, the creator of One Piece.
Databook Red, released around the time of the Arabasta arc, states that Luffy and Zoro are both “5” in strength while Sanji is a “4”. This refers to physical strength, but the M3 are all physical fighters.
Databook Yellow, released after Enies Lobby, states that Zoro is as strong as Luffy -- "stands shoulder-to-shoulder with Luffy".
Conclusion on official materials: they state plainly that Zoro is closer to Luffy than he is to Sanji, as well as that Zoro is on the same level as Luffy in strength.
6. Overall conclusion
Points 1, 2, 3 and 5 all weigh in clearly in Zoro’s favor. Point 4 about portrayal is closer but also favors Zoro when viewed holistically and taking significance of scenes into account.
When you look holistically at the entire evaluation, a pattern emerges and this also underscores the conclusion on portrayal.
1. Zoro’s character is much more about strength than Sanji’s.
2. Zoro’s role in the story is much more about strength than Sanji’s.
3. Zoro’s actions in the story are more focused on strength than Sanji’s.
4. Zoro is stated in official materials to be closer to Luffy than to Sanji.
It would at this point be extremely odd to the point of being bizarre if Zoro was closer to Sanji in strength than to Luffy, and wasn’t more than trivially superior to Sanji strength. There is literally nothing in any of these 4 aspects that supports that. So what this indicates is that it is not the conclusion we should draw from analyzing their portrayal. The portrayal in itself favors Zoro being closer to Luffy and what we can draw from every other aspect of character, story and complementary materials goes hand in hand with that
Oui. 
