PSP vs PSVita

I have a psp 3000 myself and I do indeed think that it's a great handheld gaming device, though I have recently gotten a bit tired of it because of how outdated the hardware is. Im simply looking for a new more powerful device, preferably a playstation. So my only option seems to be the ps vita, how does it compare in power against the psp? If you own both, which of them do you like better and why, would you recommened a vita to me?
thanks