I also have both a 16 GB Touch and the fat PSP. Both have internet, so that's no problem. Both play videos great, it's easy enough to convert videos to put on either. The PSP uses Memory Stick Pro Duos, I gave a couple 4 GB sticks that work out great for my needs, but if you get an 8 or 16 Touch that's all you have.
If you are into such things, the PSP firmware is fairly easy to hack, to be able to play downloaded games. Many people (*cough* myself included *cough*) do this and play emulators like SNES or Genesis, or even full PSP games by simply downloading the game ISOs off torrent sites and the like. This is an edge the PSP has.
If you really like to stay organized and have a Mac, if you use iCal, iPhoto, Address Book and Safari a lot, then the iPod is really useful as an organizer, as it can sync up easily with all those programs and keep you organized on the go.
Both have their useful features, what it boils down to is priorities.
Games? PSP.
Music? iPod.