At first, I thought you talked about 1st party games and here I agree that Sony experimented more on PS2 and PS3. But seeing that you're also considering 3rd party games, I don't really know how you manage to only find "boring FPS stuff".
PS4 (and PS3 for that matter) has a lot of different games (also some fun shooters). Some suggestions:
Plants vs Zombies: Garden Warfare 1+2:
great list! thanks