Some factors to consider:

Playstation TV is cheaper... however, not all games are compatible with it. Games like Gravity Rush and even Golden Abyss (if I remember right) use the touch controls and so they aren't compatible with the system.

PS TV can play on the big screen... but how will the vita/psp/etc games look on it? I don't think I've heard how the games look blown up on that.

PS TV uses the Dualshock 4.

I'm personally in a position where I'm all about portability. I don't really play my games outside of the house, but I like to be able to move around my house and still game. The Vita allows me to do that. I can also still remote play/play vita games if people are using the tv. The Vita fits my needs, and it's pretty much my go to system right now. The PS TV seems like a nice little system though. Just keep in mind that not every vita game is compatible with it.