I bought all my PSP games digitally. When I bought the Vita, I just put in my username & password and I could redownload them all.
I bought DSiware games and then lost the DSi before getting a 3DS. Shit out of luck.
Who wins?
Don't lose the things you pay for and take better care of them?
I mean, I'm not doubting your situation (and shit does happen), but there's a difference between not being able to redownload games and not being able to have the ability to play any of your currently owned PSP library on your Vita.
Digitally, both systems have functions to transfer/download your digitally downloaded content between systems. Depending on regions/system, you may need to take more steps than the other, but they both have these features built in.