The Golden Animation, simply put, is all the scenes from the updated rerelease from the game, animated and stretched out a bit.
As opposed to the strange combination of social life, school days, and vigilante-Shadow-fighting-crime-solving that was Persona 4, Golden, when taken at face value, comes off as a typical Slice-of-Life with a mystery sub-plot that isn't even explained well. Which is admittedly understandable, though it doesn't improve the series.
Our returning characters have their previously established relationships hinted at, as with their slightly more complex personalities, but they're mostly shoved to the side to make room for the amateur poet amnesiac with enough tsundere to give Ms Rin Tohsaka a run for money, Marie(a.k.a. canon love-interest). The series has no direct focus, but Marie's story in context of this expansion, translating to giving the girl some memories that might jog her old ones.
Cue the beach.
As a fan of Persona 4, I can admit that I found it enjoyable to watch, though that might have been somewhat mitigated by the conscious knowledge that I was supporting the ludicrous overmilking of Persona 4 that still continues with its yet to be released PS3 port and Rhythm Game spinoff. Even if the new artstyle took a moment to get used to, they were the guys who did the cutscenes for the game and they weren't too shabby here, either. Props, Madhouse.
I say watch the aforementioned episodes because they have direct relevance to the original Mystery/Reach Out For The Truth story by offering a look from the killer's eyes through the whole story; from before the murders to his inevitable defeat by the heroes.
Aside from that, though, I can only recommend this to someone who has already seen or played the original story and wants the canon equivalent of a fanfiction added on. I have no malice for this series, no anger with it that motivates me to give it a low score. But it just doesn't do anything noteworthy aside from the moment in its midpoint where it briefly returns to its source material to do what one might have wished at least half of the episodes had done. Perhaps it's for the best, though. Golden did have a happy & satisfying alternate ending, though.
Live long and prosper! :)
