Which to buy - DS or PSP?

I don't know which to get. The things I like about the DS is the split screen and the stylus. The Thing I like about psp is the better graphics. I do think the graphics on the DS are very basic. But I like games such as Deal or no deal, which isn't avaliable on the psp. I like simulation games such as sims ( I have it on pc, so wouldn't want it on a handheld.) I think the psp games are aimed more at guys. Like warcraft stuff etc. What can anyone advise me to do? I have a ps2 by the way and only have a few games for it.