I have a PSTV, Vita, a New 3ds, and am a crazy person so I feel qualified to answer this.
Get a New 3ds. There's some real dope games on it and you're not missing anything on the Vita that you couldn't play on your PSTV. The only touch-based games you might miss out on are things like Tearaway.
Plus, I've had limited success with remote play on my Vita. I need to be in the same room as my PS4 for it to work. Granted, I have bad internet throughout my house.