My son has a PSP and we messed with it quite a bit in terms of exploring it's capabilities. I was looking for a replacement for my Palm Tungsten C and the PSP was looking promising. The problems (and major distinction from a PDA or 770) with it are threefold:

1) No Bluetooth. This severely limits you in terms of peripherals.
2) No touchscreen (see other posts for why this is debilitating).
3) Closely controlled and sealed software architecture. Sony methodically closes off the hacker entry ports as the hackers find them.

Many PSP owners lament #3 incessantly, just like some 770 owners do about how UMPC's and PDA's are superior to it. One has to consider function: the PSP was designed (and marketed, mind you) as a game and multimedia device. Just because it shows elements of being "like a PDA" does not mean it is one and does not mean that Sony has any obligation whatsoever to provide you with the options to make it one. Likewise the UMPC, which is a PC.

Not to belabor this, but the 770 is sort of "none of the above". It is an Internet Tablet and an excellent one at that. it is also a next generation phone. As such, it's phone roots mean that it has PDA features (contacts, calendar, memos, etc.). Since it is a next generation phone, it also has PC features (simply by necessity).

Many errors, of a truth, consist merely in the application of the wrong names of things--Spinoza