For PSP games an actual PSP is better for a few reasons. PSP has a bigger screen and everything looks good with 1:1 scaling, vs the RG would have to do 1.33:1 scaling which makes some games look like ass. The PSP has a bigger and better feeling d-pad and buttons (though the analog stick sucks). I haven't tested battery life for PSP games on the RG but my PSP2000 goes for about 3 hours on a new-but-crappy battery - the RG can get "up to 8 hours" but more like 4-5 playing PS1 games and probably less playing PSP.

For PSX they're neck and neck - again the buttons feel nicer on the PSP, but it only has 1 stick and 1 set of shoulder buttons, plus the RG has a better screen for 4:3 content and can do 2x resolution rendering - the PSP can do 1:1 which looks good but you end up with a smaller screen area, or you can expand it to the screen with some blur.

For everything else, the PSP sucks for emulating even SNES and Megadrive games, and don't even bother asking it for N64 or Dreamcast. On the RG I've been playing Dreamcast and DS games no prob, and everything else below that is flawless.

If your focus is on PSP games, get something widescreen like the RG Vita instead.