I've been reading a LOT about this stuff on 5e forums, especially here, and so have some opinions to spout.
Linear Warriors, Quadratic Wizards is a very well-established trope of D&D, and it's still a bone of contention even in 5th Edition. Oddly enough, 4th edition was probably the best at keeping parity between classes, because of its power structure. Even then, wizards came out on top in terms of utility and flavour. Being able to inflict ten different types of damage, and target four different types of defensive stat, is simply better than being able to inflict one or two types of damage and target one or two defences; the wizard can avoid strengths and take advantages of weakness. Frankly, the wizard was also more interesting in fluff, because hurling an array of different spells tends to sound more interesting than a dozen ways of saying "I stab it".
So, what do I think the problems are?
For the purposes of this discussion, "mage" just means spellcaster while "warrior" simply means any non-spellcaster. Things like clerics have interesting middle grounds, but they're powerful spellcasters and that's a primary feature.
The first part of the problem is that "mages" get a whole new subsystem of the game to play with, accessible only to them. Meanwhile, "warriors" do not have any subset of the game which mages cannot interact with.
A second part of the problem is scope. There is no broad type of effect, and very few specific effects, which warriors can produce and mages cannot. Meanwhile, there are many effects mages can produce that warriors cannot.
The best example I've seen of this is someone pointing out that a high-level mage can produce an exact magical duplicate of the party fighter, allowing them to contribute literally everything that the fighter can on top of a vast array of other magical powers.
This is slightly truer in current editions. In some editions, rogues could find and disarm traps, which nobody else could touch. In practice, many traps would still be amenable to common-sense solutions, even if no rogue was present. It was also possible in most cases to simply soak up damage from all but the most lethal traps.