I would give a slight edge to Montana over Terry Bradshaw.
They both quarterbacked their teams to 4 Lombardis.
In his earlier years, Bradshaw still needed work in looking off the pass defenders and picking up receivers if his primaries were covered, whereas I think Montana developed those skills at earlier points in his career.
However, Bradshaw was more physically gifted in areas that were more applicable to football players in general, as opposed to quarterbacks specifically.
E.g.: Bradshaw was fast. He was probably better at avoiding sacks and running the ball. He was also one of the toughest and most courageous QB’s that I’ve ever seen. In Superbowl 10, he threw a 65-yards TD pass, just before he was knocked out by Jethro Pugh of the Cowboys. When durability is considered, what other quarterback could survive a tackle this brutal, let alone go on to win 2 more Superbowls?
I’d say that when their pass protections broke down, Bradshaw could run around without getting sacked for a greater length of time. If he chose to run, he generally would have gained more yards than Montana, but there was a greater chance of Bradshaw throwing an incompletion or an interception if he decided to pass instead of run in those situations.