From playing the PC version, I can safely say that the game still runs like ass. Well, it still runs better than the consoles (I get around 30-45FPS most of the time on a GTX 970), but if you are expecting a solid and stable framerate, you might want to find a different game. If you are playing on a console, the most recent patch has helped a little; you still wont be getting a solid 30, but you will be hovering around 25 most of the time, especially in crowds. The game is still laden with technical glitches such as dreadful texture pop in[footnote]And I mean absolutely dreadful. If you are looking at buildings across a river, there is a high chance that the textures will not have loaded in completely, and you will be stuck with a blurry mess of a house. Also, the faces of the nearby NPCs fail to load in unless you are around 5m away from them, otherwise you will be stuck with a guy that looks like his face is made of slightly melted playdough.[/footnote], and sometimes climbing up invisible walls, but at least you wont be falling through the floor anymore, so at least it is some progress. To make things even worse, if TB's recent video is anything to go by, if you are playing with an SLI/Crossfire setup, then the water textures are broken and will keep on flashing. To top it off, even if you do persist through all of these bugs and glitches, you will still find a terribly mediocre game underneath it all.
In all honesty, it really isn't worth your time, and it definitely isn't worth your money (I got it for free, and I was still disappointed!). Unless you are a hardcore Assassin's Creed fan, my advice would be just to go and play Black Flag again.
NOTE: The last patch for the game was in mid-December, and they haven't even issued hotfix since then. The next big update is for the (free) DLC content that releases, so hopefully they will sneak in some extra fixes then, but as it stands, there hasn't been much improvement for about a month now.