Yes, hence why it would be quite tempting to get one. Depends on if there are enough games on the Vita that would get my attention. Though I don't see that as much of a hindrance, to be honest.
In retrospect, buying the Vita gives you access to all the Persona games thus far -- The PSP version of Persona 3, for instance, it's got a lot of content that FES don't have (like the female protagonist who is considered to be a much stronger protagonist than the male by most of the P-fans on BSN at least) and it's got some upgrades in terms of gameplay and other good stuff.. Although, FES is the best way to go for a newcomer in terms of story.. because of the limitations that the PSP carried at the time, the story representation got cut down, where the 3D environment is derived solely to the dungeon crawling and there aren't any interacting 3D models during the story sections. Some of the guys here didn't seem to mind that but I know that a lot of people would recommend to the contrary, me included.. But I'm just laying out your options for you, if anything. There are a few good PSP games one can play with the Vita, along with some PSONE classics (should that interest you).
Anyway, sorry for bringing Persona discussion into this thread but I thought I should at least point this out for you. Fire Emblem Awakening is also an excellent game that I'm loving so the 3DS wouldn't be a bad call either.