I can confirm a couple of things that work or don't work on PS TV that have to be downloaded via search or the download list:
Jet Car Stunts
Titan Souls - Not on its PS Store
MLB.TV Premium - Free accounts can watch the Game of the Day for free despite the premium name.
Me and My Katamari - Uses the face buttons for right stick controls, so it's a perfect fit to remap to the DS3/DS4 right stick.
Star Wars Battlefront: Renegade Squadron - I suspect the other Star Wars PSP stuff works if this does, but I need confirmation on that. RS has alternate control options to use the face buttons as a makeshift right stick that can then be remapped to the right stick on DS3/DS4.
Run Sackboy! Run!
Switch Galaxy Ultra - Supports touch as an option, but has button controls to do everything so there's no reason it couldn't be compatible unless I missed something on Vita.
Gurumin: A Monstrous Adventure -