I think it is always important to give the main specs of the machine you are using (CPU and speed, installed RAM and so on), especially when the topic concerned process intensive video.
In terms of possible performance, using a lean Linux-based OS with mplayer, GeeXboX version 1.1 plays fullscreen DVD perfectly smoothly on my old Dell Latitude CPt, Celeron 400 MHz machine which only has 128 MBytes of RAM installed. I believe GeeXboX uses commandline mplayer in conjunction with framebuffer (rather than Xorg or Xvesa) however.
With Xorg you need to enable/choose mode xv for video acceleration on old machines (Xvesa doesn't provide video accel as far as I am aware).
Generally, I feel that is hard to match GeeXboX performance on a more general-purpose Linux (even a slim small one) however, since more processes are generally being run on such systems. I have a frugal install of GeeXboX on my system (dual-booting with TC in a PPR/TCZ configuration as my main OS) for that very reason.
Should be no problem getting smooth fullscreen DVD video on a faster machine though (I find, for example, that a Pentium III 500MHz, 256 MB RAM, and above works fine with mplayer-nodeps).