I picked one up on launch day and so far, I've actually grown to like it more than I thought I would. I pick stuff up like this for work and can write it off as research so it wasn't that big of a deal. What I can say is that the battery life isn't that short over the course of the weekend I played through an RPG (Suikoden PSOne DL) and spent close to 5 hours on it at one point without recharging (of course, when I noticed the battery light blinking, I stopped) and another after about 4 hours.
I like that there are several games available for DL although the price for a non-physical piece of software is prohibitive (at least for now). I can understand why Sony has a higher price tag on it for now because I really don't think they want many early adopters while they close out the existing older unit and UMD stock down to more acceptable levels. Sony has a history of keeping prices astronomically high until they level off stock (they're a hardware company, mainly, after all).
There are significant differences between the DSi and PSP, which allows for each to stand on its own in the handheld marketplace. Downside for the DSi is that there isn't a lot on offer for a device that has been in the marketplace for as long as it has (a couple of apps, fewer games) although the direct tie to social networking (FaceBook) was genius. I tend to use my DSi more as a journal camera than as a game device right now although I'm certain that it was not how it was intended...
I like the PSP tie in as the portal extension to the PS3 (of which I own two). The bluetooth link and ties to Skype are fun (although I personally don't use Skype) athough even with my older PSP unit, I used it more to browse simple sports news pages while on the go (before I got my smartphone) or as a music / media player. I also like the size of the PSP Go although it did surprise me at how much lighter it was than my DSi unit (almost 50% lighter).
All in all, I like it but only time will tell if I will use it very often...