The close quarters fighting sounds interesting and honestly more involved with the gameplay than freefall combat, which seems more like a gimmick way to involve the player during an occasional change of platform/arena.
Apparently, close fighting works when you grab someone and you then pull them in close. We did see Batman execute a throw in the trailer, so it seems like you have two different types of grab.
Once you grab someone and pull them in close, the player launch attacks at each others torsos and dodge, block and trade blows.
I'm not sure what advantages this will yield to a player as opposed standard combat though. Maybe more damaging moves are available in this mode of attack.
Freefall allows players to continue an attack that knocks an opponent down to another area in a combo, but the opponent can turn the tails to switch position and start their own combo. At the bottom, the player in the advantage position will land on the disadvantage player in a stomp attack.
So, that's what we can see so far. What are your ideas for how they'll work (or what you hope). I'll get back to you with mine, I just want to see others thoughts on these additions.