Here's the thing, it really depends on what games you like. I have both systems. I play my PSP more but my DS also gets a lot of play time. Mainly, there's a lot of pickup and play games for the DS, games where you jump in and play for a few minutes, win in those few minutes, then move on. The PSP also has those kind of games, but the big budget high quality titles tend to be more involved or more mature in theme.
For example, while the DS has Mario Kart DS, an excellent game, PSP has Wipeout Pulse, anothe excellent game. Both are racers, but Mario Kart is focused on shorter more chaotic racers with wacky weapons, Wipeout is focused on a futuristic hover vehicle racing circuit, both have plenty of unlockables and vehicle types.
Both systems are very mobile though. Both the DS and PSP have the ability to go into sleep mode. However contrary to common held beliefs, the PSP sleep mode doesn't drain the battery much at all.