Well, photoshop is more supported for plugins - which is probably the biggest thing. PS plugins are sometimes like a completely different package within a package. But I also find that PSP lacks a good masking tool (for cutting backgrounds and suchlike). Photoshop provides a whole bunch of ways to mask areas, the best of which is quickmask.
In general though, if you're serious about editing - photoshop outshines PSP by a huge margin in it's complexity. I've done a huge course, and still I can't get my head around all the features. I think one of my favourite tools in photoshop is the healing brush. It's amazing! I use it to remove blemishes from photographs, such as spots and scars. It takes a healthy segment of a picture and blends it over the top of the dodgy bit.
I tried to find an example on my work PC, but all my pics are edited already. May post an example when I get home.
Im sure PSP has an alternative, but I cant imagine it working as well as it does in Photoshop. I think i used PSP from version 3.01 (on floppy disk!) to version 6 - but as a photographer, I need the power that Photoshop gives me. The drawback is that it IS over-complicated sometimes, and it IS expensive.