I think there's a couple of orthogonal issues here.
One of them is the nature of interactivity in the levels themselves. There's a spectrum between having a game grammar made of distinct discrete interactive reusable objects and then building unique situations by assembling them in interesting ways, versus having (essentially) unique scripted traps or interactive things or set pieces that only show up in one place. Older action games that inspired Doom tend to draw from that former tradition; a lot of FPS games that came after Quake tended to go more down that second road. Quake's trigger system specifically opened up the door to a rudimentary kind of visual scripting that made the latter style of design more possible in a way that wasn't possible in Doom (although it was possible in Hexen via HexenC(?)). I think you could say that that style of design really came more into its own with Half-Life, which foregrounded unique interactivity grounded in very specific, themed levels much more clearly. Doom at its best seems like it's much more in the design space of, say, Robotron and old Mario games. Fewer unique set pieces, much more focus on discrete interactive toys to be recombined... and given id's background with Commander Keen and their earlier recreation of the first level of Mario 3, this design influence shouldn't be a surprise. Anyway, Quake feels like it is at the intersection of these two styles of design.
I think it is true that Peterson did try to go more down that second road of design in the episode 4 maps in a way that there was less of in other maps, and that it interesting.
But the other thing that sticks out to me more so, in terms of level design, is about the way the space is shaped. A lot of the very best Doom and Quake levels have a tendency of having different parts of levels intersect and interact in interesting, playful ways. The order that you see areas is different from the order that you hear areas is different from the order that you can attack into or interact with areas is different from the order you can move through areas is different from the order that different kinds of enemies can move through areas or attack areas. And that changes as you progress through a level, get keys, and activate switches. There's a tendency for levels to start somewhat linear and movement constrained but give information about later areas in a somewhat more non-linear, tantalizing way, and then as a player progresses, for the player's movement in a level to become more like a multiply connected graph as switches, keys, and activated lifts make a lot of one-way paths become two-way. And that style of design plays to the strengths of Doom and Quake using BSPs for levels as their fundamental data structure - BSPs specifically make these kinds of weird and surprising visual and physical intersections between areas manageable in terms of computational performance on 90's era hardware.
Whether or not someone considers the design approaches I just outlined appealing is fundamentally an aesthetic issue, obviously - there's no one right way to enjoy a game. But my general sense is that the Sandy Peterson maps in Doom and Quake tend to explore these approaches to play much less than the maps made by other designers.