I have a son who is just shy of 2 years old. So it is much easier for me to play sports games on it rather than a console because of a couple of reasons. One I can follow my son around the house while getting a few plays in. Two I can put the PSP to sleep and take as much time as I need to finish the game.
EDIT: Just realized that I probably didn't answer your question. So in general I play my PSP like a console because I don't have time to sit down in one spot for the real deal. I realize that are not as good but they are much closer than other genres. I play my DS much more like a tradtional handheld.