PSP/GO vs Nintendo DS/DSI/3DS?

I have a PSP but its broken, so it is time to get a new handheld. I am going on a trip very soon so I need a good handheld system. Im thinking between the DS, DSI or PSP or PSP GO. I like getting good games and graphics are NOT a big issue. The lack of video playing on the DS sucks but I can handle it. A portable DVD player will suffice. I am not a big fan of the GO, as I like having physical copies of games. I LOVE PSP games like God of War, Resistance, and Ratchet and Clank to name a few, but what about all those countless Mario, Zelda, and all the other Nintendo games. It is just so hard to choose. I have never had a DS before, and I only have a PSP 1000 and I have only 5 games so I have definatley missed out on alot. I would appreciate very thorough answers and answers from people with experience with the consoles. PLEASE dont answer with "PSP rocks." I really am not a fanboy for either. What matters to me are the games. Thanks alot. :)