Personally, I sit almost exactly on the fence, but with a slight lean towards PSP.
The PSP, IMO, is a far sleeker and better looking design. Also, contrary to what most people seem to think, it's pretty small (slightly shorter, but about 20mm longer than the original GBA (about the same size as the GBA-SP when fully flipped open). The screen is great; it's big, it's got great contrast, and it's high resolution for the size. The graphics are fantastic, it's got a big storage on the UMD and it's got WiFi capabilities as well as numerous others. On the other hand, we <B>still</B> don't know how long the battery will last (Sony said 2.5 hours, 8 hours, and 10 hours, all in the same sentence!) and the price could be a major sticking point.
The DS, IMO, is downright ugly in comparison. It looks cheap and tacky, like some stupid personal organiser you can buy for $5 with a little 'Made in Taiwan' stamp and no brand name. I think Nintendo REALLY ought to go back to the drawing board because I can see them putting off lots of style-concious people who want a handheld as a fashion accesory more than a gaming machine. The graphics are decent enough for a handheld, though they're well behind PSP's, and the dual screens has some really good possibilities. The WiFi seems to be taken to a greater level than PSP's (or they're just flaunting it more; one of the two), and being an instant messenger is cool too. On the downside, I can see the stylus being really REALLY annoying on such a tiny screen, and 3D games are gonna seem like hell without analogue.
But, despite which one I eventually plump for, they're both bound to be great. The handheld market NEEDS competition, because as the PSP proves Nintendo have been holding it back on a technological level.