I dont know how the PS4 works but it streams flawlessly into the Vita aswell. Pretty good techs.
I experienced lag on the Vita. Played Tomb Raider in my livingroom (which admittedly is further than the Wii U can reach) and the voices were out of sync and it would give a connection notification. The screen would glitch, too. I don't know if my Vita was connected via the systems own wireless or the internet, though. Still was pretty amazing seeing those visuals on a handheld console!
Vita Remote Play was actually one of the big things that swayed me to the PS4 instead of the Xbox One last month.