Hooked up my brothers PS3 just for the demo. Initial impressions after maybe 4 or 5 quarters:

Contact and physics in general seem alot better as mentioned. Most notably under the basket, contact layups, and especially on screens. There seem to be more minor animations when contacting a screener resulting in slowing your player down, while not completely taking him out of the picture as in 2K12. Hopefully this results in a more dynamic pick and roll game, as in 2k12 it was very binary (on/off). Again hopefully this results in more consequences for hedging screens and going over/under the screener, which would actually put those defensive strategy options that were added in 2k12 to good use.

This relates to contact, but rebounding at least I found was more fair. Sure there was the odd ball teleporting to player, but it was usually because that player had better position, which was gained because of the better physics. Also points in the paint are going to be harder to come by. Plenty of inside shots missed by LeBron, Ibaka, Perkins, definitely due to the enhanced physics again.

Speed definitely has been tweaked, players seemed to gain momentum as they moved, which could be the reason some have reported more of a 'heavy' feel to the game, not sure about that but in transition players like Westbrook definitely sprint past the Bosh's and Perkins'.

Controls: Eh, I never had problems with 2K's original setup, and it was hard to judge going from an Xbox controller to a half broken PS3 controller (analogue stick stuck slightly making triple threat moves nearly impossible), so I'll hold any bad feelings I had towards the new controls back. Regardless I think it's just something that'll take time to get used to.
I was thinking though, it's funny that one of the new features from 2K12, the escape shots (LT shotstick) or w.e they were called is basically removed due to the new controls, haven't really been able to tell how those missing shots or animations are put into 2k13. I know euro and hopstep were still added with the face buttons, but the dribble pullup ones I haven't really had a chance to play around with yet.

AI: Personally I thought there was quite a difference in AI. I saw Wade through a backdoor alley-oop to LeBron because I tried to help out with Durant a little too much. LeBron attacked the rim relentlessly, and I saw a couple nice kickouts after penetrating that I thought looked really true to his game.

Dunks: Definitely something that could change based on difficulty, but I saw too many missed dunks, which probably shouldn't have been dunk attempts at all. Regardless easy sliders fix. Moving on.

Bounce pass is gorgeous, god how has it taken this long to incorporate this into a game.

This is pure speculation, but I'm hoping late-game AI has been improved, as 2k12's was terrible (knowing when a quick shot and foul is needed by the CPU). The reason I bring this up is I noticed new animations regarding late-game situations. Durant threw up a last second shot and tried to release it quickly, the inbounding pass that rolls up the court (to avoid the clock running) has been redone, so here's hoping more focus was put into the other areas of late game AI. Pretty safe bet if you ask me.
Those are the things that I noticed, and/or care about, presentation is what it is, and has little effect on my enjoyment of the game, controls just take time to get used to, graphics looked terrible (again going from PC to PS3), blurry textures everywhere from crowd, to the player shots during the line-up, but w.e, secondary again. I will say that the jersey's looked a little too shiny, again is that really a deal breaker?