Well, not Lan, but I tried out both via Internet and an 56K modem.
Quake has a pretty old and inefficient multiplayer solution, which makes it very dependant on the player's connection speed. (the faster connection usually wins) QuakeWorld has a much more advanced networking, yet a considerable difference in connection speed still can be lethal. (Try the TC MOD Chapter Honour tho, that has a very fair multiplayer, where connection speed is not as dependant)
As to doom: that was very very primitive, even comparing with Q1. It requires a huge bandwidth and was almost unplayable.
That's all I can tell :-)