Yeah, it's a toss-up in someways, but I'd lean towards the Vita.
The Vita is very nice. The screen is about twice the size and much brighter and sharper, and it has a number of great games (Gravity Rush, Ultimate Marvel vs. Capcom 3, Disgaea 3). The PSP library is mostly complete - but there are a couple notable exceptions (Sony promises to get them soon...). Battery life is pretty decent, and it does most things a tablet does (touchscreen, Facebook, Youtube, web browser, video, music). I never use the camera, but it's there.
It is considerably heavier than the original PSP though.
The original PSP is cheaper, runs old disc games (as long as its not a Go), is a lot lighter and has a smaller footprint so it's easier to fit in a bag or backpack.
The biggest difference for me is the control. The PSVita's analog stick is much better than the PSP's - it's not stiff, much more comfortable and seems more precise. My hand got sore playing something like God of War on the PSP - that's not really as much of a problem on the Vita.