While the Swede is a magnet for media attention and often a sharp operator in manipulating it, the Cancun native is a reticent figure who doesn't seek the limelight and has grown in Los Angeles in large part because of how at ease he and his family are off the field.
Ibrahimovic and Vela do, however, share a role as difference-makers for their teams, and on Sunday they once again set alight a clasico that is fast becoming the best in MLS. The Swede and the Mexican exchanged goals in a 3-3 draw, with Ibrahimovic netting twice to move on to eight from the five "El Trafico" games so far and Vela scoring once to improve to seven.
But it was Vela, the front-runner in the league's MVP race ahead of Ibrahimovic, who provided the primary talking point this time around.
The LAFC captain threw down his captain's armband and appeared to fire off some less-than-friendly words toward coach Bob Bradley after he was substituted in the 61st minute. Vela had scored to make it 3-3 eight minutes beforehand, but looked to be struggling with injury.
"Carlos, [his] hamstring tweaked," said Bradley in the postgame news conference, explaining the substitution. "We don't know for sure. I don't think it's a real bad one, knock on wood, but we weren't taking any chances. Obviously, he is a huge competitor so he's not too happy when he comes off.
"The conversation with Carlos is what you would expect. I made the decision because I think it's the best one for us."
The desire to beat the Galaxy was at fever pitch among LAFC supporters ahead of the game. And LAFC's chances of securing a first victory over their rivals at the fifth attempt would've increased with even a half-fit Vela on the field for those last 30 minutes.
The Mexican wanted to continue, but it clearly wasn't worth the risk.
The numbers for Vela this season are phenomenal and highlight just how important he is to a side playing some breathtaking attacking soccer: Vela has 41 goals and assists in 26 games or, in other words, is directly contributing to a goal every 55 minutes this season. Vela also has had more shots than anyone else (132 to second-placed Ibrahimovic's 113), most shots on target (60 compared to second-placed Ibrahimovic's 44), is third in chances created (82) and is second in assists (15).
The last thing LAFC need is for Vela to be out for an extended period, or even to lose rhythm in the remaining weeks of the regular season, even if fans will have to live with the "you can't beat us" jibes from Galaxy supporters for a little while longer.
Vela didn't speak to the media after Sunday's game. He will likely regret the out-of-character outburst, which was caught on TV and spread quickly on social media. Bradley would be justified in feeling a little disappointed by the captain's behavior, but there may be a little part inside of the head coach that took the sulk as a positive reminder that Vela very much cares about his club.
In case anyone needs reminding, the 30-year-old's reputation, at least outside MLS, is that he isn't the most engaged sportsperson to have ever played. Vela famously said that he wouldn't be playing the 2014 World Cup even on his Playstation and that he prefers basketball "one thousand times" more than the sport he plays professionally. The narrative in some quarters was that Vela moved to MLS for money and a comfortable life in Los Angeles.
But having watched the strop, as well as the golazo and joyous performance in the thrashing of the San Jose Earthquakes last Wednesday, it is inconceivable to suggest the former Real Sociedad standout is not committed and driven to succeed in his project.
"I go out and enjoy myself," admitted Vela last Wednesday. "I'm also happy at home. I think it is important for a player. In the end, don't forget that we're people that enjoy our work, that enjoy each moment we live."
There will be those that scoff. But Vela doesn't need Ibrahimovic to tell him that MLS isn't La Liga, and his renewed self-imposed exile from the Mexico national team will always sit uncomfortably with many El Tri fans, especially when he's playing so well.
Overall, LAFC remain in a good place after the draw, and Vela's fitness is an important part of that continuing. The playoff spot is sealed, the chemistry between fans and players is there for all to see in and around Banc of California Stadium and there is a strong playing identity that Bradley has ingrained.
Winning MLS Cup is clearly the goal, but you get the feeling that Bradley, Vela & Co. would be keen on facing the Galaxy again this year and getting another chance to end the winless start to the clasico.
"Sure [I'd like to play them]," said Bradley. "It's a big game whenever you play them. We tried to take control of the game. They respond. I've watched them in a lot of games and they raise their level against us ... the matchup is good, it's good because it's two teams in L.A., two different fan bases, honestly two different ideas.
"I'm not providing all the answers, but if you look at them and what they're about and how they play and how we play and where our players come from, there are two very different identities there."
With the way Vela and Ibrahimovic seem almost hell-bent on one-upping the other in these games and the intensity of the rivalry, Bradley isn't likely to be the only one maintaining hope that Sunday's showdown isn't the last we see of "El Trafico" in 2019.