Yeah Quake, especially GLQuake, pretty much fell on(if not defined, there is probably something less well known but earlier) our side of what “architecturally modern 3d shooter” is; while Doom fell on the far side of that. Psuedo-height in the environment; most world inhabitants sprites, mouselook and circle strafing not yet a thing(though added by most of the newer engine replacements; with the effect of making parts of Doom seem way easier in retrospect; because they hadn’t been designed against an avatar with that sort of mobility).
Also some aesthetic differences: Doom was cyber-industrial-on-mars-with-increasing-evident-descent-into-hell; but Quake 1 didn’t have nearly as much zOMG-gritty-future as it’s successors(where the stroggs v. space marines thing was established); and a lot more somewhat weird medieval-ish/horror enemies(the entity codenamed ‘Quake’, that you are trying to stop, is identified as Shub-Niggurath, though Lovecraft isn’t hewed too closely to).
Also, Quake is the one that unites the NiN soundtrack and the nailgun; as justice demands.