It isn't the self-restriction bit that I'm talking about, though. That's kind of self-evident. My problem is that until higher levels, there's nothing an illusionist can really do that any other wizard can't do well enough. At 2nd level, an abjurer gets an ablative shield. A conjurer can create almost any random tool the party might need in a given situation (especially if you read "3 feet on a side" to mean 3 cubic feet in volume, allowing for such adventurer standbys as a long coil of rope or a 10-foot pole - which is also the kind of DM flexibility necessary just to make illusions viable, so I'd say it's a fair equivalence). A diviner's portent is perhaps the most inimitable ability out of all the 2nd-level abilities, potentially allowing for a virtually guaranteed miss or success at any time. The enchanter's hypnotic gaze... I'll be generous and say that's on par. Evokers can freely use AoE spells without having to worry about accidentally hitting the fighter. Necromancers can siphon out the souls of their enemies and heal themselves, allowing them to be less cautious - and while that's similar to the abjurer's ability in effect, both of their 6th-level abilities immediately make up for it. The transmuter's ability's effectiveness I'd rank as halfway between the conjurer's and illusionist's, but it is also something that lets the transmuter feel like a specialist and do something that no other wizard can really attempt. At 2nd-level, illusionists get an ability that can be exactly copied by two castings of a cantrip available to anyone. At 6th-level, they get an ability that can be decidedly distinct from other wizards, but it isn't often that it is reliably so without contriving a scenario for it to be. At 10th-level they get an ability that finally is wholly unique to them, but it's decidedly reactive, and since wizards tend to stay out of the fray, I don't imagine actually sees much use. Especially compared to other schools' 10th-level abilities. It isn't until 14th-level that illusionists actually get to do something that inarguably marks them as better at illusions than anyone else.
Had he been the only wizard in the party, this probably would never have even occurred to me. But given that there are two wizards, and that one of them is able to mock the other by doing almost the same thing without spending any extra resources... I mean, yes, that behaviour is an issue of its own, and I did already talk to that player, but... It just shouldn't even be possible to do something like that.
Anyway, I may talk to him about the sorcerer solution, since his backstory has him being a circus performer and so he also has a really high Charisma. It wouldn't take much effort to basically retcon.
TL;DR: The problem isn't so much power as it is differentiation and class identity. Until higher levels, the illusionist - in comparison to the other wizard schools - feels like a sorcerer trained in Performance calling himself a bard.