It really depends on the person, really.
The DSi has more titles, without a shadow of a doubt. The PSP has more downloadable games (and soon, every game will be downloadable), plus you have the added option of downloading PS1 games to it.
As for the
type of games, DS(i) games are generally more geared towards the younger crowd. PSP games are generally geared towards the teenage and adult crowd.
Graphics-wise, the PSP wins in this category hands down. The resolution is greater and the system has a better processor.
The DSi has a touch-screen, while the PSP has no touch features. Some games (Phantom Hourglass, for instance) utilize this feature heavily, while others (Izuna, for instance) barely use it.
A positive for both handhelds is that they are both region-free in regards to games.
Here's a link that compares some of the specs
My personal opinion is that I prefer the PSP because it has more of the type of games I like. I also prefer games with great graphics and the ability to play the PS1 games that I love. I play both, but I definitely log more hours with the PSP. ((I can get drawn into it more easily))