Much as I'd like to take the patriotic stance and say Capt. Brown shot him down, I think most of the modern evidence points to an Aussie machinegunner. Read The Red Baron's Last Flight - A Mystery Investigated by Norman Franks and Alan Bennett for a good analysis.
An interesting fact about the crash diorama - did you know that they first built the aircraft (full size, by the way) in perfect condition and then wrecked it? Used a forklift or something to crumple the wing!