Golden Animation is an alternate version of the Persona 4 anime, based on the PSVita version of the game, like a "what-if" where the main character chooses some other options of dialogue and goes for another ending. It's the same story, just different outcomes with a new character added. In video game terms, it's like New Game+, where the player already played through the game once, then plays again to see the other results.
Also, Golden Animation is both darker and more comical, albeit a lot shorter and faster-paced. Golden Animation should be watched after watching the original anime.