I can't do the whole quake I, II, III was better debate. I dig em all.
Quake 1 was insanely fast. dm4, "The bad place" remains one of the craziest deathmatch maps ever made. The single player game (remember the 'elders' zone?) was scary as shit. Face it, in quake 1 when you get hit by a rocket you *know* it. Oomphf.
Quake 2 was different for sure. More open so it felt slower but once you got deathmatch going the speed picked back up. In Quake 2 when you get hit by a railgun, you *know* it. Oomphf.
What made quake 3 was the maps. Tourney5, DM17 "longest yard", Q3DM13 and some others were just great maps. Nice flow, nice balance, fast, fun.
I was playing Quake II's q2dm1, "The Edge" remade in quake 4 over the weekend. Still a fun map. The new graphics don't add a lot to the fun tho. I'm not sure If a remake is needed. Just play the original.