I would go with the PS Vita because my pc covers the parts of the 360 library that interest me, I like the PSP already, and Vita will interact well with my PS3. However, if you really love Halo--really, really love it--then the 360 might be the better choice for you.
Something else to think about: Do you have consistent access to a television or other screen for a full console, or do you have to worry about inconveniencing other people? Vita is a much better "anywhere, anytime" gaming device, and its library will grow soon enough. Of course, if you wait a bit, it's tech will likely improve (battery life, etc.), and you would have the 360 in the meantime.
At least you have options. Hope you enjoy whatever you finally choose.