persona 3 and 4 are the ones in the series that deal with social links and progressing throughout the school year.
I'm a fan of the series and yes, if you can drop the money on the vita, P4G, and a stupid vita memory card. It's worth it.
It's just unfortunate that the Vita is basically a Persona 4 Golden player at the moment. I havent seen many other decent games for it yet.
With Golden, they added a couple new social links (and a stable of personas to go with them), a motorcycle, simple gardening, more fishing, and different classroom questions.
with all this extra stuff, you also get to go out and roam the streets at night to increase relationship points (daytime links only rank up in daytime)
and depending how you finish, you get to continue your S.Links through January and part of February.
Chie got a new voice actor and it's spawned thousands of forum pages of debate from absolute love to absolute hate. (Personally it's growing on me and I like it.)
Also, Teddie got a new voice actor for it as well, but I dont think anyone has cared. Over all, I dont feel he's as annoying as he used to be, but he says the same lines, so~~.
Also I believe more lines are voiced overall as well.
All this stuff adds at least 30% content to the whole game.