HI!
The beauty of watching the Duke is that He was such a great actor that you could Believe that was really him! In most of his movies, i felt that could really be him! ( the person he was portraying)! I didn't get that feeling watching his cop movies. Not bad movies, just not high on my list.
The only movies I feel that John simply wasn't believable in are Dark Command and The Conqueror.
As for Brannigan, I totally believed that John Wayne could be that cop, and besides that, his chemistry with Richard Attenbrough is the highlight of the movie. Despite all that he had gone through John Wayne was never less than completely believable as a threat to criminals.
It would have been better is he had done this movie in the late 50's early sixties, but westerns were still his bread and butter.