LOL How many of these DS vs PSP threads are we gonna start?
Use the search button people! lol =3
Anyway, I'd go for the DS all the way!
As Tidus says, it can do everything the PSP can do! Only reason people support the PSP is cause its made by Sony, and most people are of the opinion that Sony is more mature than Nintendo. Of course I've seen a lot of things to the contrary... but whatever...
If you take some time, and actually search for the stats on both systems, its clear that they both do just about the same thing... The DS has a little more features (that are actually usefull) and the PSP has a little better graphics.
Honestly, anyone that wants to use the PSP to watch those ridiculiously expensive UMD movies that you can't use anywhere else, are wasting their money.
Most of what I've seen out/coming out on the PSP is just series remakes of other games currently on the PS2. Only game on it that I want is Lumines. Most the games on the DS (the ones that aren't made by Nintendo) are new and original, and more are on their way. Where as, what I see coming to the PSP are still remakes. =/