On my eeePC 1000HA, I run full GNOME and full KDE without a problem and even
use Compiz. I don't do a extreme mulit-tasking or heavy processing chores,
because I use it for light tasks such as reading RSS feeds, listening to
podcasts, email, e-reader, etc. I have not tried to max it out.

I am not sure about your problem because I gave up on UNE early on. It is
slower than GNOME with Compiz. Mutter, the window manager, is to blame. When
Natty comes out, Mutter will be history on Ubuntu. Unity will use Compiz and
Unity 2D will use Metacity. It costs nothing to try out another desktop,
except the time. You can have more than one installed. You could also look
at XFCE and LXDE.