BBAJ is a far better show than American Idiot, in my opinion. They're not exactly easily comparable, though. American Idiot delivers basically what it promises.
I saw Bloody Bloody last night. It is interesting to note that they have made several changes to the script regarding Native Americans (the character of Black Fox was originally Black Hawk, a very real person who did not do what the show depicts, for instance). There was apparently quite an issue regarding the Native American community and this show while the show was at the Public.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."