The DS. Over 100 million sold worldwide, and there's a reason for that -It's fantastic.
The DS, in terms of hardware, lags behind the PSP, but this really doesn't matter. If you wanted pretty graphics then you'd buy a PS3, not a handheld. And DS games certainly don't look bad. From hardware-pushing, cutting edge games like Dragon Quest IX to traditional spriteling games like Valkyrie Profile, the DS has some great looking games on it.
The console is extremely well designed, too. Very stylish in any colour and very comfortable to hold, the DSi is a big step up from the original DS and by far and away better than the PSP. The extra screen space on the DSi (3.25" as opposed to 3") is also very welcome. It doesn't sound much but it makes a difference if you play a lot. The DSi also seems to have better speakers than the DS and DS Lite.
The games library though, is the biggest draw of the DS. It has an incredible lineup spanning every genre. From epic RPGs like Dragon Quest IX and Final Fantasy IV, to lighter and more casual games like Nintendogs. The DS library is incredible and anyone who likes games should experience it.
If you're even considering buying a DSi, then do it. You won't look back.