I run Ubuntu 8.10 on a SSD on one of my eeePCs and on a hard drive on the other.
However, it is hard to compare because they have different processors. The SSD
one has a Celeron processor and the other has the Atom. I suspect that the SSD
would run as fast if it had the same processor, but as it is it is a tad slower.
I have eeeBuntu installed on a SD card on the Atom based one and it runs as fast
or so it seems, but it is optimised for the netbook, so again it is hard to
compare. Both computers have 1 GB of RAM.

My opinion based on subjective evidence is that there would not be much
discernable difference. If you are looking for a performance edge, you would do
better to use a specially optimised distro and a faster desktop such as XFCE,
Fluxbox or LXDE. I suspect that if you had your swap area on the SSD it would be
beneficial.