I just swapped out my Pi 2 for my Pi 3. I haven’t tried too much yet, but I ran a few N64 games and they run a bit smoother than they did on my overclocked Pi 2. Nothing earth shattering, though. Still have to fiddle with the rendering engines to find the one that works best for each game, and there are still certain spots in certain games with major slowdowns (mainly cutscenes). I’ve also set the resolution to 320×240 for all N64 games. I have yet to mess with any overclock settings on the Pi 3.
I also played through World 1-1 of Yoshi’s Island, and it appeared to run flawlessly.
I never had issues with PSX games on the Pi 2, (granted, I haven’t played many of them) so haven’t bothered testing them on the Pi 3, since I’m assuming they’ll run just as well.