I would go with the DS Lite. It has the GBA compatibility which gives you hundreds of more games to choose from. It is also really cheap.
For me, the DSI is a complete waste of time. It plays the exact same games as the DS Lite.
It has slightly larger screens, but not enough to make much difference. It has lower battery life. It has two crappy cameras, both have worse quality than you would find on an average cellphone and it isn't really used in any games worth having, just for silly stuff like "take a photo of your face and stretch it around with the stylus" which is fun for about 5 minutes.
It has downloadable games, but they are mainly very simple ones and there hasn't been a killer app released for DSIware to date. Half of them are crappy versions of alarm clocks and calculators featuring Nintendo characters and aren't even games.
The music player is pretty meh, because the DSI doesn't have great speakers. Any ipod blows it away. The internet stuff is pretty terrible and slow.
It also costs a lot more money than the Lite.
Another thing to consider, is that it is likely Nintendo will likely create a new portable system in the next year or 2. Might as well go with the cheaper Lite now, and wait for the better new system.