I've never tried the DS Browser, but the PSP browser is pure own. From what I've heard, the DS browser is too slow, but I'd imagine it's comparable to the PSP's. I was able to handle 56k all those years, so why wouldn't I be able to handle a slow connection on a handheld? Either way, I think the concept of using the internets on the go is sweet.
The main advantage the PSP has over the DS, IMO, is that the PSP browser is free, while the DS's is like $35 USD. Like I said before, I've never used the Opera browser on the DS, but I've heard it's slower, (would anyone have expected anything different?), which I have no problem with. It's not like I would even try going to YouTube or anything like that....a handheld browser is simply a convenience. As you said, you can check out Wikipedia while taking a dump.
What's not to like? Oh yeah, the price...now I remember.