Both were drafted young (18) and then played their entire rookie seasons at age 18, which is rare. Both did well as rookies. I'd probably call their rookie seasons about even.
Over the span of the first four seasons of each, Yzerman takes the clear edge, mainly because his 2nd year was also really good (MacKinnon's was a bit disappointing) and because he started hitting his prime in year four (1986-87, 90 points, 12th in scoring), which MacKinnon didn't (2016-17, 53 points, 72nd in scoring).
In year five, MacKinnon's surges up to 'super-elite' status and he's been there ever since. Yzerman did the same in year five, pacing for 63 goals and 128 points (but he was stopped after 50 goals by a serious late-season injury). Yzerman then took the scoring up to an even higher 'super-elite' level in year six with his 155 points (highest total EVER by non-Gretzky / Lemieux). (In fact, in that one season, he was matching Lemieux / Gretzky in ES scoring.) Yzerman more or less maintained the elite-level scoring between 1987-88 and 1993-94, with a degree of injury in the first and last of those limiting his totals.
Injuries have more notably limited MacKinnon's totals, but certainly since 2017-18 he has been elite every year, with amazing scoring totals. It's also impressive that (what is seemingly) his peak offensive season just occurred in year 11. That's quite rare.
So, that's where each player sat/sits after 11 NHL seasons. (I'm suggesting it's really only fair to compare with Yzerman in 1994, when he was at the same place as MacKinnon now.) Up to 1994, even though Yzerman was respected as a great captain, there was starting to be a suspicion that he couldn't win it all in the playoffs (later proven wrong), whereas of course MacKinnon won it all at age 26, so if there were any doubt he removed it a bit earlier.
So, up to age 28 and each guy's 11th season, I would give a very slight edge to MacKinnon. But it's a hair's breadth between them. And of course MacKinnon had a Cup by season 11, which Yzerman didn't.
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As to how their careers go after season 11, we can only speculate for MacKinnon. Yzerman passed his scoring prime after that very season, but he continued to be a strong offensive producer for about six more seasons (taking him to age 34), which was really impressive. Even better, he had those three Cups and at least two legendary playoff performances in '98 and '02.
If next season (and the next few) were to show that MacKinnon's scoring peak is over (and he drops to, say, 9th in League scoring for a couple years before declining) and if the Avalanche never win the Cup again, then I'd have to guess the pendulum of comparison would then start to swing in Yzerman's favor. (After all, Yzerman was an out-of-nowhere 1st team All Star -- for the one and only time in his career -- at the age of 34!)
Despite coming in on a pretty bad team (one of the worst of all time in 1985-86), Yzerman actually had a very fortunate career in terms of his team's building around him. By his year four, his club was at least competitive, and they were strong in year five. Then then dipped for just a couple of years, but then suddenly Lidstrom, Fedorov, etc. start arriving. And just at the moment when Yzerman's scoring peak ended, his team surged to the top of the NHL around him (finishing 1st overall the very season Yzerman's was first past his offensive peak). So, in a way, he had one of those "charmed careers" where his team's success around his aging body kind of made him look a bit better than he really was in his latter years (a lot of players have the opposite -- for example, Howe and Gretzky).
Anyway, I'd say MacKinnon for now (after season 11), but the jury's out after this point. Yzerman still may win the race when MacKinnon's career is over. Depends on how things pan out.