If I was to buy a game for my Playstation3, but I also wanted to play it on the go, would this mean I would need two copies? Or is there some kind of system that means I don't, maybe a system similar to Remote Play which could work anywhere due to 3G.
It can't. But some games will come with PS3 and PSV versions that have some compatibilities. Check for each relevant game - it's possible some will be packaged with a copy of both PS3 and PSV versions.
Surely if they're bragging that the games will be as good quality as the PS3 versions, they'll be able to be some kind of 3G cross-over to play both? The reason it couldn't be done through Remote Play on the old PSP's was that the PSP couldn't handle the visuals.