If a title exists on both systems, I'll choose the Vita. The better screen, the second analog stick, and the possibility of capacitive touch is a no-brainer. (For the life of me, I can't figure out why Nintendo didn't include a second analog stick on the XL. It looks like there's enough room.) In general, libraries on Sony's platforms are more my taste. (I've owned about an equal number of systems from both companies over the years.)
Out of curiosity, which handheld do you find better, the Vita or the 3DS?
For myself, I didn't buy the 3DS for the 3D because, as I predicted, having strabismus makes it virtually impossible to benefit from it. The 3DS does seem to get better battery life, though, and it's easier to turn off the wifi.
Vita does has proper support for achievements ("trophies"), while 3DS does not.
The 3DS murders the Vita in the area of backwards compatibility. Vita can only play a subset of PSP games, and from what I hear, it doesn't have much support PS1 classics or minis. I still have my PSP-3000, so this doesn't affect me.
As media consumption devices, there's no comparison. Both have browsers and Netflix, but Vita now has YouTube and lets you play videos from the memory card, plus there's PSN movies. Netflix on the Vita's OLED is gorgeous and YouTube app is quite good. For watching movies, I use whichever system happens to be charged at the time.
EDIT: I forgot to mention that the Vita supports background downloading--both of games and downloads in the browser.