Vita can play digital PSP games, but PS4 can't play PS3 games. Why would Sony make one system BC but the other one not?
Vita can also play movie and music files and view photos, in addition to its myriad of non-gaming apps (maps, email, Facebook, Twitter). PS4 can't do any of that stuff. It seems Sony didn't plan PS4 development very well when their handheld has more features.