Xandros is much lighter and the eepc can run it well. Putting a full distro UI may be a bit sluggish unless you fine tune it. I had a coworker who had one of those and he spent quite a bit of time because the Xandros installed was too limited for him. He did get Vista running on it as well at one point so when I say it was sluggish, it can still be quite usable.
It really depends on your system specs. I have an EeeBox that came with Windows XP home that runs great. My little box has an Atom N270 with 1 GB of RAM.
Ubuntu should run just fine on your system. If you have an USB optical drive you can download the installation media and run it as a live CD without installing Ubuntu. This way you can test drive the OS before wiping your system. Keep in mind this will run slower than a local installation.
@b and @Ivan have given you the right answer. Xandros is certainly not the way to go. Test drive the Ubuntu live CD and, if you like it, do the full install. Forget about Xandros; it has no socially redeeming value.