Which device is better?
Is the quality of video better on the i pod touch?

If you really want PSP games and are buying the machine mainly for games, PSP. If you want an organizer where you can check your email, surf the net (if there's WiFi), maintain your calender, and have many other useful applications (there's pretty much something for everyone), listen to music, and watch videos buy the Ipod Touch. It not only does most of those things as well or better than the PSP, it's also a lot more compact to carry around. There are some good games, but to the best of my knowledge, nothing that would be on par with a PSP retail release. It just depends on what you are looking for in a device.

I'd go with an iPod Touch because you can get most of the iPhone apps for it.

for Multimedia (Music, Photos, Videos) the iPod's quality is unbeatable... on the gaming side, the PSP is slightly better as far as my experience goes... none of them matches the DS, but gaming is definitely the iPod's weakest point.

Multimedia Purposes: Ipod Touch

Gaming Only: Either one, but the Ipod Touch is recommended (from my POV).

PSP Games: PSP (no duh)

PSP. I have an Iphone and to be honest the games are a little bit overatted, the lack of d-pad and buttons really is a hindrance. That's if your just getting it for playing games, otherwise the Touch is great.

The PSP is awesome and there are some awesome games on it, buy the PSP!

PSP if your wanting quality games, dont mess with the iPod Touch, get a iPhone.

You can not go wrong with either, but do not underestimate the amount of quality, cheap games on iPod touch.
I hope that this little warning does not sound too dramatic, but the most important thing to remember if you do buy an iPod touch is make sure that you buy either the 32GB or 64GB models.
Do not purchase the underpowered model. If you want the best performance of games, the 32GB and 64GB specs are boosted to equal the iPhone 3GS capabilities, which are at least twice as fast with far better performance for games and general App load times.
I realise that it is more expensive, but the games are becoming more CPU intensive and to draw the most out of the likes of 'Asphalt 5' and the forthcoming 'N.O.V.A, you would want the higher spec version.

I'd go with the Ipod touch because of better music listening and movie watching. And of course all the great cheap or even free apps and games.