But they're both full bands. Each has a unique sound. Brass bands & concert band brass sections sound different, mainly due to cornets instead of trumpets, tenor horns instead of french horns & more in the barri/ eupho/ tuba lineup. I especially like the oboe sound in a concert band. Wouldn't fit into a brass band (except maybe as a soloist).
I cop the "brass bands are only 1/2 a band" all the time from concert band people. This is not so. They are just different to concert bands.
