Nothing happens. Your account is for the Playstation Network, NOT the specific console. You'll have one account that goes across three pieces of hardware; The Vita, PS3, and the PS4.
Your PS3 games however, will not play on the PS4. That does not mean you need a seperate account. This question has been asked many, many, MANY times, and it's still the exact same answer.
This thoughts been bugging me. So we all know our ps3 account will transfer to our new ps4's. we also know we cannot have the same account on 2 different ps3's. For the many of us who plan on keeping our ps3's to play our older games does this mean we'd have to start a new account on the ps4 or would it be where we just couldnt be logged in at the same time?
Another question. Just say god forbid the ps4 is having issues. You send it in but your really hooked on playing destiny. You buy the ps3 version to hold you over. Or maybe its dcuo. Regardless our saves are on a server. Can we play our save on the ps3 while we are waiting for our ps4.
Hmn, sounds like it was your question to me. As for being logged in at the same time, we don't know yet. And since those games will be two different versions, no you will not be able to pick up a game that you started on the PS4, and continue it on the PS3.
It would be unlikely, considering two PS3's on the same account cannot be run at the same time.
Also, while some games will be multiplayer PS3 and PS4, other games may not be.
I highly doubt the PS3 version of BF4, for example, will be able to play with PS4 users (The PS3 version only supports 24 person multiplayer, the PS4 version supports 64)