Euphoniums are usually bell up instruments, as seen in the picture. In normal four valve euphoniums, the fourth valve is alongside the other 3 valves. The only compensating horn that I've know to have the fourth valve besides the other three is the Canadian Brass insturument, a small production line put out by Wilson. Baritone horns are much like euphoniums, though they are a tiny bit smaller, lighter and have a sharper brighter sound. The baritone was invented after the euphonium, mostly, I believe, for marching purposes.
Most baritone horns have the bell curved forward to help project the sound.
Baritones usually don't have a forth valve and I've never heard of a compensating baritone. I've never played one much. There are those who argue that the only true baritone is the English baritone, like this one pictured. I've never played one before, but I believe that they are smaller brighter versions of the euphonium. Mr. Bowman is one of, if not the finest euphonium players in the world.