On the whole, Quake is a rough franchise with ups and downs. Doom maintained a solid level of quality throughout even if games like Doom 3 were divisive, but Quake changed so wildly judt from Quake 1 to Quake 2 that its hard for me to stay as positive.
Quake 1 is probably my fav FPS of that decade. It is full of weird issues like a lackluster weapon roster, spawns being a positively evil and unfinished enemy type (in general it still needed 1 or 2 more enemies to round the roster out) and not really diving into its mythos or enviornments in the interesting ways that even Doom 1 and 2 did. But man, the atmosphere is just so damn sublime that I don't care. The Strogg and more generic setting of Quake 2 and 4 is deeply uninteresting to me, but Quake 1's mix of sci-fi and low fantasy is such a treat. And though I love the ost for Quake 2, Trent Reznor's ambient work on Quake 1 is some of my fav FPS music of all time, honestly.
Rambling aside, whilst my bias towards Quake 1 and high preference and nostalgia for yhe multiplayer suites of Quake Live and Champions make me want to pick Quake, I think pound for pound Doom is the better franchise, at least for single player.