If I recall, the PS4 controller can simulate either the front touch screen or the back touch panel, but not both at the same time. So games that require both are incompatible. Thankfully, very few incorporate both features; some games that do have been released for the PS4, like Gravity Rush.

Overall, it's a wise idea to use a PS4 controller on the PSTV, and if you plan to do the remote play thing, connect the PSTV to the internet via an Ethernet cable.