The campaign has a place in my heart too, even if it's not perfect. A lot of DOOM's level design was predicated on claustrophobic interiors, and when you go "outside" in many levels it feels like a glorified courtyard. From the very first level, Quake 2 pushes hard to create an illusion of environmental complexity that plays very distinct from Quake 1 or DOOM.
Go here right now and play a few games against bots and people of Quake III and UT99: https://dos.zone/mp/?lobby=*
There is no denying that movement and gameplay is much more enjoyable in Quake compared to UT. Even with the lack in variety on all fronts.
QIII while solid feels missing lots of flair, it feels more generic shooter. Good, solid, but a little generic.
Q2 was always my favourite, that's where I started my multi-player journey. I only played against bots in the first Quake, and only played against my cousins at their place in Doom (they had multiple computers linked up back in the day).
Although, to be fair, we played Doom over an RS-232 cable - hauling a PC across the city every weekend was a testament to our love for the game :)