Objectively speak Bloomberg was pretty decent for the poor, the outer boroughs, the artists, and many other groups that he's accused of screwing over. The reason for all the vitriol is that he wasn't suitably enthusiastic -- he didn't pay all the required lip service, he isn't perceived to feel people's pain.
Just to take one small example, De Blasio talks about the two New Yorks, but meanwhile he took a lot of money from the large taxi medallion owning companies, and is threatening to close down the new apple green outer boroughs taxis. That's a program that unequivocally targets the "other NY".