I've played a few more hours since I last posted, enough to get more of a free reign on the first dungeon and my first taste of night exploration. They've made some interesting changes to the game.
Combat is basically the same as before. You wander around floors of the dungeon, try to hit enemies that you come across for a player advantage, and then take advantage of their weaknesses for easy victories. So far, Shuffle Time is less shuffle and more like they give you a few cards to choose from that feels more like what they did in Persona 3 (or maybe it's just in Portable) with Coin, HP/SP recovery, weapon, and Persona cards in the mix. P4 just had Persona, blank, and penalty cards from what I remember, so these can help extend your stay in the dungeon than before.
Camera controls are a little weird from my experience. You can choose between using the shoulder buttons or right stick, but one is inverted while the other isn't. There's an option to invert/uninvert them, but that just reverses the situation. The camera control works fine, but that odd quirk bugs me when it's not the same for both.
They just introduced costumes with the introduction of the night town exploration, which features a little segment where Morooka calls you to meet him at the gas station so he can give you a package. This seems to be like Persona 3's armor that sometimes changed the character model in dungeon/fights but this stuff is just a visual look without stats attached to them at the moment.
They've also tweaked Personas a bit so that there are now skill cards that you can use to enhance a Persona's abilities like in Persona 3/Portable.
From what I've seen of the trophy list, anybody that gets a platinum would need to put some serious time into the game to get everything they require.
There's an interesting new feature making use of the new network functionality that lets you see what other players have done on that same day. On the first day that this is available when you first get the option to do whatever, about half go into the TV and the other half spend time with Marie, the new S. Link character.
You may notice a trend in this post, as Persona 4 Golden so far seems to be a mix of the best parts of Persona 3/Portable and Persona 4 with some further enhancements beyond that.