Portability (size / weight)
The Playstation Network Store. That is possibly the best (and most underutilized) feature of the PSP. The ability to seamlessly transfer video content with no conversion to your portable from your PS3 is pretty much awesome. As far as games, the PSP has had its share of gems...just not enough of them. Most tend to come from Sony in-house studios. Third party support has been sporadic and inconsistent (excepting FFVII Crisis Core and the upcoming FF Dissidia and a handful of other titles from xSEED and NIS). The real strength of the PSP comes from its feature set. Video and audio playback (though the audio is mostly a joke), Skype, a passable web browser, RSS feed reader, internet radio, picture viewer, direct access to the PSN Store, remote play with the PS3 (limited, but nice). All these things add up to a robust user experience that Nintendo has failed, thus far, to offer with its sub-powered DS.
Oh, and why they still haven't added a second analog stick is beyond me. PLEASE, stop trying to do FPS games on this system! THEY. DON'T. WORK.