A few things I've noticed, both from my own play and my reading of others' posts:
* I seem to have more "mass combat" (ie PCs plus warband, vs NPC warbands) in my Prince Valiant game - which is a "lite" and "indie" system - than I've heard of in any D&D game. Mass combat is the only subsystem in Prince Valiant, and is the most complicated part of the system, but I think no more complicated than D&D combat.
* When discussion on these boards turns to actions declared by players for their PCs that have the aim of persuading or converting NPCs, the response from D&D GMs seems to be to set the bar for successful action declaration very high. This gives me the impression that games GMed by those posters probably don't figure much switching of sides from bad guys to good guys, which is a pretty standard adventure story trope.
* The flipside of the previous paragraph is conflict among the good guys. By logic this should be rife even among D&D parties: we have paladins hanging out with the Grey Mouser, and devout adherents of multiple religions (paladins again, clerics, druids, etc). But the approach to play that
@Campbell is calling "mainstream" doesn't seem to accommodate this terribly well.
The notion of
flexibility is itself pretty flexible. In the context of the discussions Campbell has referred to, it's normally being used to talk about the content of RPG fiction rather than the processes of RPG play. I realise that Campbell is trying to open up the notion, but even sticking to that focus on
fiction, it seems to me that a flexible RPG at least should accommodate some thematic variety - both in trope, and in theme in the stricter sense - and the attendant variety of conflicts - in terms of methods, stakes, participants - that would correlate to that thematic variety.
Under that conception, I think the most flexible RPG I've played is MHRP/Cortex+ Heroic. It can move from pretty light-hearted to a little bit serious (not as serious as, say, Burning Wheel) across multiple fantasy and superhero tropes, with conflict in various arenas for various stakes, and with the protagonists in various relationships from opposition to loose cooperation to tight parties.
I've also, back in the day, found Rolemaster fairly flexible - it's skill system is clunky by modern standards but envisages conflict being resolved in a variety of arenas, and when we played regularly we would use the Depression crit table from RMC3 to apply consequences for emotional conflict as well as physical. But (consistent with
@Manbearcat not far upthread) the system needs a degree of GM force, plus understandings from other participants not to lean too heavily on its points of vulnerability, to work. (It has a cooking skill, but no resolution table for that skill and no cooking failure crit table.) Of modern games the one that reminds me most of RM is Burning Wheel. I think that's another very flexible system, but it doesn't have as much published for it as RM ended up having and so to push to its full flexibility will rely on the GM using the extensive system hacking advice to build appropriate subsystems. Even without that hacking, though, I think it covers a pretty wide range of FRPGing ground. In its heyday I think AD&D aspired to the sort of fictional range of RM and BW but never got there because of the failure to support out-of-combat conflict resolution. I don't know 3E or 5e as well as AD&D but nothing I have heard about them suggests they're very different from AD&D in this crucial aspect.
To conclude a meandering post, I think Prince Valiant is an amazing system - Greg Stafford's best work in my view - and I think the lack of its widespread uptake is one of the tragedies of RPGing. I think it's very flexible across a very wide variety of non-modern RPGing, though it doesn't have a cooking skill. In play it can range from lightly comedic to deeply intense and character-driven (not as much as BW, but at least as much as 4e D&D). What it's missing is a subsystem to support player-side magic use, which might be seen as a limitation.