Took a Level in Badass: Not that he wasn't badass in the first game, but in the second game, he guns down scores of undead pirate gangsters with a tommy gun.
Took a Level in Jerkass: Edward is noticeably angrier in the 2008 reboot, swearing and being rude all the time. Justified in that he's got amnesia and has no idea what's going on and would understandably be angry about.
Demoted to Extra: Emily is a playable character in the first game, completely absent in the second, and returns in a supporting role in the third.
Purely Aesthetic Gender: Playing Emily features exactly the same gameplay and levels as playing Edward. It only affect the opening text displaying the player character backstory, and a couple of comments when interacting with items in the manor.