With comparisons to AC, HP, and DPR between builds being a fairly high source of contention when talking about balance, I feel like the community is split between what they want from Asymmetric Balance vs Symmetric Balance.
The definition of balance I've encountered that I've found the most useful, goes something like this: a game is better-balanced the more choices it presents to the player that are both
viable and
meaningful.
Edit: Fingers slipped to upload prematurely.
Asymmetric Balance is such that one character might have higher AC and HP, but lower damage while another might have vice-versa.
I'm afraid that sort of balance would tend to present a lot of less viable to non-viable choices, depending on context.
D&D has certainly tried for balancing that way a lot over the decades, and has consistently failed. You can look back over D&D discussions, and find the Martial/Caster Gap, LFQW, 5MWD, and Fighter SUX discussions longer than there's been an internet.
Symmetric Balance is such that all characters have similar statistics between each class, but approach them in different ways. Example: Fighters might have equally high damage as wizards, but fighters are doing it with single-target attacks and wizards are doing it with AoE (this is a theoretical and not how it works in 5e).
The danger here is that choices will turn out to be less meaningful. If you all ultimately
just degrade the big bad's hp at the same rate, what difference does it make who is playing what?
D&D only really tried something that might have been classed as symmetric balance once, in 4e. Like 3e, 4e put all classes on the same exp level chart, and like, 5e BA, 4e put all characters on the same basic level progression as far as d20 bonuses were concerned. Where it really mattered tho, was resources, and for the first 2 years, at least, all classes had a rough parity in unlimited, n/day and n/encounter resources. 4e avoided making class choice meaningless only at a very high price in development effort (and retaining some asymmetry!). Each class had hundreds of unique powers - the fighter and wizard, each had more powers than 5e has spells, in total. And Source radically differentiated sorts of powers, the wizards
spells were implement powers that attacked no-AC defenses, the fighters'
exploits, weapon powers, that mostly attacked AC, and so forth...
But, arguably, even 4e had a deeply asymmetrical aspect in formalized Roles, that differentiated classes within a Source, as well - ironically, it wasn't anything new, D&D had always had distinct duties for the "Big 4" - fighter, Cleric, Magic-User, and thief - it had just never managed to make them more or less equally important before.