You can see how similar the instruments are when you look at them, but you'll notice a few small differences:
The Euphonium has a bigger bell (opening) than the Baritone
The Euphonium's tubing starts out skinnier and keeps getting fatter as it wraps around itself. The Baritone's tubing basically stays the same until the bell starts to form and gets wider
The Euphonium sounds more mellow and warm than the Baritone, which is a bit brighter and cuts through ensembles more.
Listen to this beautiful love song performed on Euphonium.
David Childs, one of the best Euphonium players in the world, plays a piece called "Czardas."
Check out this Baritone Solo that was arranged from the "Nutcracker" ballet!
There is a different type of Baritone Horn made for Marching Bands that are held more like trumpets. Check out a demonstration of a marching Baritorn Horn in this clip, as he plays the theme song to the show "Arthur."