All of which is to say that if the game is perfectly balanced (as posited), all the choices would be meaningless options from the power-gaming perspective, wouldn't they? Because no choices you made would affect the efficacy of your character. Or am I missing something?
That is, roughly speaking, the conundrum at hand. Perfect balance would require uniformity in all things. Practically speaking, there are two paths to meaningful customization, which don't (severely) affect power balance.
The first path is to have several options that are each comparable, from a power standpoint. Damage types are an example of this type of customization. Bludgeoning damage isn't better or worse than slashing damage, but it's different, and you may wish to choose one or the other depending on various circumstances. In earlier editions, you also had the choice between high crit-damage and high crit-range (or both, but less base damage, or other features); weapons in both 3E and 4E were designed around the idea of these trade-offs, where everything was close
enough that none was clearly better (at least in a vacuum). But then, once you factored in feats and abilities and whatnot, it usually turned out that there was one or two clear winners (again), and the meaningful choice was gone. (It's not impossible to maintain that level of balance, and keep the choice meaningful, but you need to be super careful to not then include feats or powers that push one out ahead of the others).
The other path to customization is apples-and-oranges. If you have the choice between learning a damage spell, a healing spell, or a charm spell, then none is better than either of its alternatives (from a balance perspective). Even if the damage is more or less than the healing, whether the charm lasts a minute or a week, the effects are simply not comparable. A potion of flight is not comparable to a potion of fire resistance. There's a lot that you
could do with this sort of customization, but the interdependence of stats in most games means that it's usually inefficient to multi-task.