From my experience people who say psp is "shit" are Nintendo fanboys and if that's the case, I usually don't even bother because there's no reasoning with a Nintendo fanboy.
I get just as sick of this response -- it seems that it is just a convient excuse to dismiss people who are interested in the DS.
I desperately wanted another handheld outside of a Nintendo produced one to succeed in the past. I owned a Lynx, GG, and NGPC (and a Wonderswan after I purchased a GBA) before I ever bought a Nintendo handheld. I love 2-D titles. To me, the Gameboy Advance and DS were the last bastions for traditional sprite driven 2-D. Sure there are some that pop up on consoles, but they are far and few between. I might also add I was not interested in the DS in the least when it launched, but there is a reason why Nintendo handhelds do so well outside of what you see as pure fanboyism. They are quality machines. The machine with the best specs doesn't always win, especially in the world of handhelds.
Nintendo also builds quality hardware for the most part. I am extremely careful and protective of my junk. I purchased my PSP brand new, and it had severe issues crashing and locking up from the get go. I also worked at GS during the PSP launch and saw numerous units returned and exchanged. The PSP unit feels rickety in my hands and it bugs the hell out of me. You can call the DS gimmicky, but the PSP employs just as many 'gimmicks' to attract sales.
Many people on my course say the DS is brilliant and the PSP is shite. But guess what? They all own PSPs.
Or most people you know that own PSPs also own DS units. See how that works both ways? I would think you would rather they own both to make a proper assessment.