In my opinion there are two ways the answer to this question can go:
In terms of speed, getting around, ease of use, etc, the winner is: iPod Touch, by a long shot in my opinion. The internet is much faster on the iPod than the PSP, it is easy to navigate (main reason being the touch screen, I think) and overall I think it is just a lot better browser to use. With the PSP it can take so long loading the pages sometimes that I would rather just pull out my laptop and get where I need to go quickly. With the iPod it is quick enough and easy enough that I have found I didn't even turn my laptops on this weekend because I could do my normal weekend browsing on my Touch.
In terms of connecting, the winner is: PSP. I have had a lot of problems connecting to the internet. When I first got it on Friday I was shocked because the internet worked so well. Anytime I wanted to get online, or check my mail, the weather, etc. it was right there and updated. I never had a problem connecting or anything, it worked as well as my Blackberry, where I have internet just about anywhere with my cell phone plan, but obviously I wouldn't have as many places I could connect. But I quickly learned how fast the battery was draining while using apps, internet, etc. I remembered reading on the forums that turning the wifi off really helps to conserve the battery, so I went ahead and turned it off, thinking whenever I planned to get online I would just flip it back on, not a problem. However, after doing this a time or two I began noticing the issues. Every time I turn off the internet, it can take several attempts and sometimes I cannot even get reconnected to the internet. It will show that I am conncected to my internet and everything, but when I go to check the weather, it says update failed (also does this with stocks) when I check my e-mail it just keep spinning and then says it failed, safari won't open pages and says it is not connected to the internet. Sometimes it will start working after I try a few times, other times I will have to wait and go back to try and get online. Not sure if this is just a problem with mine, but it has become a bit of a pain.
If it weren't for the latter issue, then the iPod Touch would win hands down, in my eyes, but since I've never had an issue connecting to my internet on the PSP, it gains some points there.