Showdown is a black-and-white Western that showed in New York City in 1994.
The Trio were thrilled by it when it came out, particularly Broadway. Unfortunately, his overenthuasiasm about a gunfight in it led to his accidentally shooting Elisa with her own gun afterwards. ("Deadly Force")
The film was scored by Ennio Morricone. 
Showdown presumably showed at the same theatre where the Trio later watched Bambi. Brooklyn described Showdown as "a new Western", though whether he means it was actually produced in 1994 or was simply new to the Manhattan Clan in the same sense as Shakespeare was a new writer is uncertain.  One could guess that it was the former and that theatre specialized in showing older movies since Bambi was not produced in 1995.