The PSP is more of an evolution of the GBA, it continued the push towards matching console level graphics and continued to have a large number of ports from the previous gen. The GBA even had carts that played cartoons and tv shows, similar to how the PSP UMD's had movies.
The DS and 3DS rely much more on gimmicks of dual screens and 3-D, instead of pushing the graphics and entertainment hardware.
That being said, I love the DS, 3DS and PSP. Once the Vita becomes a JRPG treasure trove like the other 3 systems I will be happy to purchase one.
I never really enjoyed my PSP all that much and I love the Vita. Biggest reason for that is the hardware itself. They tried to do console-style games for the PSP, but in my opinion even the best efforts were regularly sabotaged by the lackluster control options the hardware was able to support. Loading times were generally awful as well. Think Wipeout 2048 is bad? Play some early PSP games. I also didn't really care much for the types of games most PSP users were so crazy about. Monster Hunter? Dissidia? All those strategy rpgs (unless their names started with Jeanne and ended with D'Ark) - Just not my cup of tea at all. The system peaked super early for me with Wipeout Pure and a bit later when Ready At Dawn released Daxter.
I already own more Vita games than PSP games, and I imported my PSP from Japan because I couldn't wait. --- "When I became a man I put away childish things, including the fear of childishness and the desire to be very grown up. -C.S. Lewis