My impression is that they're both mostly hated by the populace of the city, though reading Adams's indictment I think he might have been actively trying to unseat Rudy for the title of worst mayor of NYC
And Adams is indicted because he accepted tens of millions of illegal campaign donations and other bribes from foreign businessmen in exchange for giving them perks in NYC (including doing things like trying to intimidate the FDNY into certifying unsafe buildings owned by said businessmen)