You really don't see a difference between the 2012 Thunder and the 2014 Thunder? Just for starters, one of the two teams has a vastly-improved Kevin Durant who's going to be named MVP in a day or two. I'll leave it to you to figure out which one that is. 
But seriously, the 2014 Heat are worse than the Heat we saw in 2012; not even just off record alone, but from the actual contributions of the players. Also, again, the Clippers aren't a grind it out team; that's not really how they win games. They win by overwhelming you on the offensive end more often than not.
No, I don't see a difference in their style of play. Of course some of their players have grown but I don't see how their style matches up any better than it did then.
Experience. Experience is always important in the playoffs. Experience is why teams like the Thunder can advance over the arguably more talented but inexperienced Nets.
Also, part of the reason why the Heat beat the Thunder was because of Brooks' insistence on not going small. When the Thunder went small, they were insanely effective against the Heat; this was seen as recently as this past season when they blew them out in South Beach - without Westbrook, mind you. As long as Brooks is willing to swallow his pride and make the necessary adjustments, the Thunder have a better chance against the Heat if they meet in the Finals again.