I have the Asus EEE PC 1000H. If you have large hands the extra width of the 10″ netbooks is nice. The resolution is the same between the 9″ and 10″ displays.
I can’t complain much about the performance. It handles the usual surfing, word processing, and mulitmedia apps just fine. In fact, my Dell desktop took a dump a couple of days ago. I used the EEE PC as a replacement just fine. I connected the VGA port to my 20″ LCD. All I had to do was select the correct resolution. Even dual display using the netbooks LCD works. I even had OS X running on it for awhile.
The 9″ will be lighter and easier to carry on your travels. The Aspire One is feather light but, felt “cheap” to the touch. If you’re into modding at all, the Apsire is less mod friendly.