Every character feels like a reskin of eachother, so I think different levels of agression and different ways to catch the player off guard in a chase would do wonders for the fun factor of the game.
So, right now, all the characters are basically the same, Peterson is the brute, Gerda is the brute, Nielson is a slow brute, Otto is a brute with a gun, and the Mayor is also a brute but a bit faster. I have a few ideas for attack patterns unique to each character.
Mr. Peterson will be clever, being able to quickly swerve and go in strange, inconsistent directions to surprise the player and cut them off. The longer he has chased you, the more angry he will get, picking up items and throwing them at you to hinder you further.
Gerda will be more persistent, chasing the player for longer distances, and her speed will increase the longer she is chasing you.
Otto will be mostly the same, but will only use his gun in situations the AI feels is practical. If the player is swerving between tables and ledges, he might save his shot for when the player is more vunerable in tighter areas.
The Mayor will be incompetent at chasing on his own, but he might call the police to come to his house, adding a second enemy to deal with.
I think Officer Neilson should stay as the basic character, with no special abilities as he is basically the AI tutorial.