I find myself working this way: I really tend to prefer games that have more "gamey" elements to them on portable consoles and things that are slower in pacing and maybe not as deep story-wise. I get really into tactical RPGs, lighter RPGs (Super Star Saga, for example) and puzzle games and such. I don't care for time wasters so much, but I really like having something that I can play at my leisure pretty much anywhere.
When I'm at home, I like the more cinematic stuff. Action RPGs, shooters, nearly anything unless it's got a fairly slow pacing. Then I either want to have it on PC or the ability to carry it around with me and play it procedurally.
Unfortunately, I haven't really been using my handhelds very much lately, but I find that I tend to have more memorable experiences with some of those games and kind of enjoy that freedom of taking a game with me. I like handhelds a little bit better, but there haven't been as many games on handhelds that I end up wanting to play. :(