The bottom line: Nintendo's DS is far better designed and constructed. Never mind the specs and features and games, the DS hardware isn't as flawed as the PSP.
Read on for details.
As an interesting aside, a little birdy told me a Nintendo PR flack, when pressed about the GBA cart slot in DS game cases, mumbled something about the DS being able to access both the DS and GBA carts at the same time, and that there are plans for expansion cards for the GBA slot with software in the DS slot. Therefore you might conceivably want to keep your GBA-shaped expansion cart with the DS games. Therefore, two slots.
Now if only there were good DS games to play...