I have for some time been mulling over ideas for a fantasy RPG, and some of them of course concern balances.
The "zero to hero" (and thence to superhero/demigod, and perhaps beyond) aspect of D&D is most evident in the level scheme. Most RPGs since have, by one means or another, incorporated this emphasis on the pursuit of more strength, skill, and other forms of innate power.
Metamorphosis Alpha and Traveller were among the notable departures. There were significant (and pretty random) differences among characters from the start; characters could in the course of play acquire mutations in the former game, and skills (perhaps including psionics) in the latter; and, of course, there was high-tech gadgetry that offered various advantages analogous to D&D magic items.
None of those, in my experience, weighed as heavily as D&D levels (or skill ratings or other equivalents in other games). There was not such an issue of matching scenarios to characters, or characters to other characters. A newly generated persona could easily be played alongside those that had been in play for a long time, and casual "one-shot" games were facilitated as much as ongoing campaigns.
It was of course a matter of degree rather than absolutes, and gear could count for much; someone running around in powered armor with a ray gun was obviously a "combat monster" whenever it was feasible to bring those to bear! Social and financial power also tended to be greater among players who had been some time at accumulating it.
So, one thing I have been thinking about is setting aside the "getting better all the time" rat-race of a bigger + to hit, to damage, to defense, to skill, to muscle, etc.. Produce adequately competent or "heroic" characters, and pretty much leave those ratings where they start. The rather "iconic" results might be in keeping with the way many protagonists in fantastic fiction are commonly seen. It certainly rings a bell for me when considering classic comic-strip/book and radio/television characters (who, for commercial reasons, must retain easily recognized characteristics even for audience members not versed in all the serials' continuity).
Characters might learn new skills that increase their versatility and reflect their growing biographies. Spending a lot of time among sea rovers, steppe nomads or rain-forest hunter-gatherers would be an example. On the other hand, characters might "get rusty" with skills long unused.
Such factors might be described not in terms of bonuses to binary (pass/fail) rolls, but differences in results. For instance, it might be in some cases that anyone can get something done -- but the specially trained can do it more quickly. The products of their efforts might be more precise, durable, reliable, comprehensive or elegant.
Magic might likewise emphasize expanding qualitative capabilities. Limited numbers of uses (as with potions, scrolls and "charged" items in D&D) would bode against perpetual accumulation, as well as making use a strategic factor and acquiring magic a common goal. More interest, in both game and "story" terms, could come from trade-offs that make magic not an unadulterated boon.
The more all this ties into particulars of the world and the characters' adventures in it, the more it is likely to add in really character-building terms. That is to my mind the greatest reward for long and successful play: the depth added to a character's emergent story.
In a sense, perhaps the balance that matters most is among players' opportunities to add to that.