i usually prefer emulation, but only if it is is (nearly) 100% compatible (with the game in question), and the speed is (nearly) 100% (on the PSP), or more than 100% (on the PC).

On the PSP, I prefer emulation over console because its portable.
On the PC, I prefer emulation over console (sometimes) if there is the possibility to speed up above 100%, hack (as in cheat), or other nice features, and sometimes because of the controls or the screen size, e.g. with gba games i hate looking at a non-backlit tiny screen.

I prefer the console when the game is modern, e.g. PS2/NGC/XBOX and up, because these games are of high enough resolution to be worth playing on a TV and the controls are better on the console because of the analog inputs. Also, theres not much point in playing them on the PC...