Body is different (bigger, different battery door, slightly different eyes in terms of the board).
Bolt is different (Axe bolt can be field stripped w/o tools as it has a button release which is nice)
On/Off ASA on the Axe
Trigger is different
Boards are actually the same depending on when the Axe came off the line. Both can use the same board, and until recently they both came with the Optimus board (now the Axe has the Shockwave).
I'm sure there are other things, too, but that's off the top of my head.
Here's my Mini/Axe combo side by side to give you an idea.
Having shot them both recently, the Axe (this is off memory) seems to have a little less kick and a different sound signature. Most likely just a combo of the body size/weight/extension. Could all be in my head, too. Who knows. lol.