The graphics are disappointing, the limitations of the 360 are starting to show. Not sure how the PS3 version looks but I can't imagine it's substantially better. Honestly, if the PC version is a choice for you, I'd wait. Although RE5 looked pretty damn good on the 360, it looked quite a bit better on the PC, graphically. The facial animations, however, are superb. By far the most noticeable improvement in the game.
It differs a lot from RE5 gameplay and co-op wise. Capcom, for whatever reason, removed so many of the co-op mechanics that worked. I'm sure for those who prefer the single-player won't mind, but it's disappointing for me 'cause the co-op was something I actually enjoyed. The only co-op that remained are the opening of doors or boosting up a broken ladder or across a gap. It's rather disappointing, really. As I said previously, the gameplay is a bit disappointing as well, feeling a lot heavier with the gun vs. gun fights. I haven't played Chris's campaign but I've heard it's the best for boss battles. However, Leon and Helena's boss battles were pretty damn awesome. As for Jake and Sherry's, they're shit. At one point you're fighting against... wait for it... a tank.
Controls are essentially the same, with a few additions, like the cover system. They did make it a bit more action-oriented in regards to the melee combat, which I wasn't too fond of. I prefer RE5 because it was a nice middle-ground between survival and action melee - you stood in place while slashing enemies. In RE6, you can get away with mashing the melee button to kill hordes of zombies, even on Veteran difficulty. The UI is still very similar with some aesthetic changes between campaigns. Well, similar when playing, slightly different when you're in your inventory or the pause menu. I did enjoy the slight changes between campaigns though, made it feel just a little bit more fresh.
As for weapons, mostly usual suspects. I don't think I've used them all yet, but the additions aren't anything amazing. Which brings me to the new skill leveling system. They completely removed the stat leveling for weapons, and replaced it with a list of skills you can unlock and sometimes upgrade. For example, you don't increase the stats of each weapon individually, rather you unlock the skill that improves your weapon damage as a whole, and it has three levels. That's it. Honestly, it's shit. They allow you to equip three skills together, and eventually give you the option of creating up to eight different sets of three skills. You're able to switch the set of skills at any time, but quite frankly, I couldn't be bothered. To make matters worse, it takes a lot of skill points to unlock the upper levels, so it feels like the progress is incredibly slow which made it quite frustrating when you finally finished a chapter after an hour or so.
Annnd that brings me to the chapter select. They seem to have decided against breaking the chapters up and giving you grades per section. Now, you play for at least an hour, often quite a bit longer, and get graded. The problem with this is that if you haven't put aside enough time, you may be forced to quit before you finish a chapter. All this feeds back into the frustration of slow leveling. Two hours before you finish a chapter isn't bad if you've got the time but sometimes you just don't. I suppose it's possible that it won't take as long during second or third playthroughs, what with you getting familiar with the progression, but still something I noticed.
Oh, the inventory system... I could be wrong, but I did Google it and couldn't find a way to trade items. Now, items that are in boxes, chests or that are dropped by enemies are picked up by both players. So, again, they've removed a more co-op oriented mechanic (that of deciding who uses what weapons, and who carries herbs or first aid sprays, etc.) and replaced it with something that just feels stupid. You also pick up the skill points from enemies. So, sometimes you'll pick up a handful and your partner won't. With the larger enemies, it's guaranteed, but with the smaller ones it seems to be completely random - another thing I wasn't fond of. Not having to manage your inventory with your partner or divvy items up, it meant that you could use any weapon you wanted, so long as you had the ammo. The idea sounds good but the problem is that if you're not paying attention you'll often find yourself with a full inventory, and rushing to dispose of an item in favor of something on the ground. Oh yeah, and you can't drop it... no, you dispose of it.
New Game + means that you carry over what unlocks and upgrades you've chosen from your skill list. So, essentially, NG+ is what you're playing after you've finished one campaign. This means that if you go from Chris's campaign to Leon's, you'll still be playing NG+. I don't like the skill system but at least they did this part right. I couldn't imagine having to restart the unlocks with each new campaign. Weapons aren't carried over though and they vary slightly between campaigns. Specific weapons for specific characters, while others are available to both.
Any other questions, I'm happy to answer.