Eh, maybe I am just olde - cause the load times never bothered me - and PSP offers a lot of RPG titles that DS doesn't (and vice-versa, but I was more drawn to the former titles) like the Persona Portable series (in particular) the remastered Lunar game (nice game), Tactics Ogre and all the PS1 Final Fantasy games/not to mention other PS1 RPGs. And while I'm not someone that needs super high definition graphics - the smoothness of the sprites in a lot of the remastered games is SUPER NICE. I mean I do notice and like it, and am willing to sacrifice a second or two every 10-20 minutes for it. I recognize other people don't feel the same way, but that's just the way things are - people value different things.
(And seriously, a lot of stuff looks utterly terribad on DS)
I also like the thing where I can turn off my PSP when I'm playing a game, and then turn it on to be right where I left off.
I only play games on portable systems and my computer, so that probably changes things a bit for me. If I had a PS3 and could play all my downloaded games on it, I might choose to do that... but honestly, before I got my 3DS I was playing DS 1 time for every 9 times I was on my PSP (and sometimes I was playing GBA games on my DS). Game quality has a ton to do with that. No RPG on DS so far has compared even slightly with the level of engagement I've gotten with Persona portable 3.
I also dug the fact that I didn't need a hack chip to put TV on my PSP. Netflix on my 3DS has improved things on that front, but if I go on a trip where I won't have access to internet, the PSP will still win on that front. That said, at least the video quality on the 3DS is better than the utter crap quality of video on the DS.
Also I agree on the UMD movies thing... what a rip off! Way too high priced and really, how many times will you watch the same movie? They need to think in terms of "how much money is a person willing to pay for two hours of entertainment with limited replay value?" but they failed to do so.