Can you even mention them both in a same sentence. I mean, PS3 is proper game console, PSP is portable, mobile solution. Two very different things...
For me, PS3 is really the best if you want for a very good game experience. But if you want for portability where you can play anywhere, go for PSP.
PSP because it is easy to take with you. I dont have time to stay at home. But i always take my PSP with me.
If you have a budget you can buy both. Like me, I have PS3 and PSP. I'm using my PS3 when I'm at home and having a great time playing it on my 56" LCD. While I enjoy using my PSP when I'm traveling in some other countries.