All the NRA outdoor bullseye matches I know of are three-gun, smallbore, centerfire, and bigbore. I guess you could just shoot two of the three individual matches and not be in the aggregate, but there is really nothing to worry about with the .45, especially if you handload.
It takes a darn nice 9mm to be competitively accurate for bullseye. There are a few places accurizing Berettas for the separate Service Pistol "leg" matches and you can get a 9mm set up for PPC which is nearly as demanding as bullseye. The S&W model 952 gets good reviews.
IDPA is what we used to call a "combat" match before we got politically correct. Targets are large and close, times are fast, and there are different divisions for anything from 9mm or .38 Special on up.