Its all opinion based. Not everyone has the same opinions, that's why we find it a bit awkward when people don't like the system we like.
I like the DS better because its' games keep me interested more. Does this make the PSP bad? No. I'm 100% positive there are people that don't have the same opinion as me. For the technical side, I pretty much have music, video, internet etc features on other devices I own, so I have no need for an all-in-one device at the moment. Does this make the PSP bad? No. Others probably don't have music, video, internet etc on other devices and prefer to have them on an all-in-one system. I actually think the PSP is great because of that, and it's probably the most lease expensive all-in-one device out there, it's a great deal.
Now, i'll give you what you want to hear/see:
I'll admit it the PSP is technically the superior system, it's a fact. It has better graphics, and way more features for a great price. It's overall a better deal than the DS. The PSP does ALOT more for just 40-50 dollars more. Now how could anyone prefer the DS to the PSP? Well that kinda goes back to what I was stating in the beginning.