Persona 4: Golden is an absolutely amazing game that I own, built off a great series, and I can say that I wish I had started the series sooner. I really wanted to rate this game because of how much I love it, but this is going to be my first review, so please don't expect anything great.
Summary: First off, this is a remastered version of the original Persona 4 that was made for the PS2, so the game is going to be rather similar, but still have quite a few new additions/tweaks that make it better in every way when compared to the original. The game is basically a visual novel mixed with an RPG that is not unlike the Pokemon system, of which you use [monsters] to fight your enemies.
Graphics: The graphics are honestly not the best. Compared to a slew of other Vita games, Persona 4: Golden is rather on the lower end, but it still doesn't look absolutely horrible. The visuals are definitely improved over the original, with a more crisp, and vibrant feel to them. Despite the game's lack of superior graphics, they really don't detract from the game itself as a whole.
Sound: The game has a wide array of music and sounds that play throughout. There are different sound tracks depending on the time of day, location, and action that the character is performing. There would be something different if say the character were fighting an enemy, or simply talking to a friend during the daytime. The sound has a certain level of detail, and it's rather excellent.
Addictiveness: As soon as I started to play this game, I couldn't put it down. Everything about it kept me in a trance and wouldn't let me stop playing. The game had a hold on me, and before I knew it, I finished the game for the first time with a total of eighty hours already put into the game. If I had the time, I would play this game repeatedly just to see everything I could do differently during the course of the game. It's really fun, and really addictive, but also very long, so I wouldn't recommend it to someone that doesn't have a decent amount of spare time on their hands.
Story: I really don't want to give out any plot points or spoil the story here, so I'll just say some basic information. You play the role as a high-school second year male that moves to the town of Inaba. You meet some people there that end up becoming your best friends and you spend a great deal of time with them (Most of the game, really). Some events happen and you gain the use of Personas, of which you use to fight certain enemies. I don't make the story sound all that great, but I really don't want to ruin it, the game has a really strong, elaborate story, and I would hate to spoil it all.
Depth: Depending on how fast you play, and the way you play, it could take you anywhere from 30 -100+ hours. If you're just planning to play through the story, it would take you a lot less time than someone who were to try to complete the game in its entirety. It also depends on if you're speed-running the game or not. It took me an extra bit of time because I was playing it slowly, taking my time, fully experiencing and enjoying the game. I even listened to all of the characters when there was vocal dialogue.

All in all, it's a rather full experience.
Difficulty: I gave the game a lower score, but I guess it can vary from person to person. The game itself could be difficult to learn for some people, and others could pick up the system and really quickly understand everything about it. There's also options for difficulty, so difficulty is really hard to measure.
This is my favorite game of all time, and I would seriously recommend playing this, or, if you do not own a Vita, to play the original PS2 version. It's an extremely memorable experience, and if you have the time, it is well worth it.