Quake was better for multiplayer though. Personally I enjoyed Quake 2 the most. Quake arena was designed for multiplayer but you had to practice with the cheating bots so it was kinda boring.
Quake 2 multiplayer is such a blast. The cat-and-mouse chase fights in that game is what defines the genre of "arena shooter" for me, there's still nothing else really like it.
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.
IIRC, my problem with Quake multiplayer was that one node acted as the server, so when I connected to a friend’s computer via modem, my lag was a serious disadvantage (neither my friend nor I ever won as clients). Doom, on the other hand, simply froze both computers whenever there was a communication issue.
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 :)