I haven't noticed much change between Pre and Post New52 Batman but I'm also not the biggest fan. How do you think he's changed? Wonder Woman and Aquaman on the other hand, feel like whole different characters to me.
Yeah, that's a a valid point of view. I will try to explain my own.
With Batman there is no single obvious change, but there's a confluence of smaller changes--many of them to characters besides Batman himself--that have the aggregate effect of changing who he is and how he fits in the universe.
For example, aging Dick Grayson up (he became Robin at sixteen now) while aging Batman down has affected the nature of their relationship. With the compression of the timeline it becomes difficult to see the familial relationship that Batman previously had with many of his team mates. Tim's banishment to Teen Titans means Batman has virtually no relationship with him at all.
Typically, Batman has also been written with a younger, less experienced attitude. This is particularly true in Snyder's material. While I actually approve of Batman being written in a more human manner (and I like the increased relevance of Bruce Wayne), writing Batman as being in his late twenties aggravates the disconnect between the character's youth and all the strings of his history they tried to keep together in the New 52.
A great example is the Batman written in Tomasi's Batman & Robin. He seems a completely different character from the one depicted by Snyder; older, more contemplative, fatherly--and the only version who seemed to give a damn for more than one issue after Damian died.
Which brings us to Damian. There's a reason he never appears in Snyder's batbook (or really anywhere outside of B&R). He doesn't fit. Snyder doesn't include him because his rash, younger Batman makes no sense as the father of a ten year old.
In this way, the difference between old Batman and new Batman can be understood as the difference between Snyder's Batman and Tomasi's Batman. One is young, brash, runs a little hotter and is generally more inclined to solve problems by the seat of his pants. The other is older, colder, more calculating, but also the patriarch of a family he's built around himself in a way that grounds his humanity.
Both fine interpretations, but certainly different characters in the details.