Bradley's claim to fame is a good win over then unbeaten Peterson, giving Alexander his first loss, getting an atrocious decision over Paq, earning an undeserved trilogy because of that, a "warrior's win" over Provodnikov, which should have been another loss, and then a deserved close decision over roided Marquez coming of KO6. On paper he looks much better as in reality, as both Alexander and Peterson didn't turn out to be as good as advertised at the time, and the officials beat Paq and Provo for him. I don't think he would be able to deal with Crawford's size, reach and power advantage at the weight. A guy like Peterson, who has about the same dimensions, lacked that power and skilllevel, so he's no comparison.
Bradley was an underrated fighter (I thought he lost the first fight to Pac but it was closer than many believed) and had good skills. He would be competitive against Bud for awhile.