Photoshop Elements is Photoshop with all of the image creation stuff ripped out. It still has all of the photo manipulation stuff in it though. What this means is that you wont be able to make those crazy pure photoshop images you see all over the net, but it will do you just fine for photo editing. I know a couple professional photographers that use it.
I dont have any experience with PSP, so I cant comment on that. Were it me, I would go with PS Elements, but that is just because I am familiar with PS and know how to use it
If PSP is the more powerful piece of software, you may want to go that route. It would probably be wise to see if you can find someone with one or both of them so that you can tool around and see which one you like better.