Like the PSP before it, the PlayStation Vita can access content on a PS3 and even play PS3 games remotely.
Remote play PS1 games on Vita from a PS3. I only recently discovered that this works and I'm loving it. : r/gamecollecting
PS Vita Standing Dock for HORI Remote Play Assist (6J9GSWRJS) by RetroMetro
How to Play Music on a PS Vita Game Console
PS3 hack opens up console library on PS Vita - GameSpot
PS Vita Hacks: How To Connect PS3 Controller
Why the PS Vita still matters in 2015
How to Play Your Own PS4 Games on Your iPhone with Sony's New Remote Play App « iOS & iPhone :: Gadget Hacks
Using the DS4 controller on various devices (PC, PS3, Vita, Android)
How to Use PS4 Remote Play - PlayStation 4 Guide - IGN
This is the closest you'll get to a PlayStation Vita 2