Flugabone was designed for marching bands (I believe), and has a slightly larger bore than a typical valve trombone or bass trumpet. 
 
Valve trombone 
Bass Trumpet 
Flugabone 
Baritone Horn 
Euphonium 
Marching Baritone 
 
They're all the same length of tubing (so pitched the same), just wrapped differently, and with some variation in the bore size and shape (more cylindrical, for valve bone and bass trumpet; more conical for Flugabone and Euphonium). 
 
The instrument Maynard played is a SuperBone, which is BOTH a slide trombone, and has a set of valves, so it can be played as either instrument, or in combination. 
 
MF also played a crazy horn called the Firebird, combination of slide and valve trumpet.