Not all groups have these instruments. Some that do will expect separate parts for baritones and euphoniums; other groups will expect only one part. You may want to check before writing parts for a particular group. Orchestras generally do not have baritones or euphonimums, but you can count on military and marching bands and wind ensembles to have them. Some groups treat the two instruments as interchangeable; others (particularly in Britain) do not.
Of the two instruments, the euphonium is generally considered the solo instrument, because of its sweet, mellow timbre, which is very different from the more direct, brassy sound of the trombone, the other brass instrument that shares this range.
Most of these instruments are pitched in B flat (in other words, their no-valves harmonic series is based on a B flat), but they may or may not be transposing instruments. Parts for these instruments may be written as non-transposing parts in bass clef, or they may be written in treble clef for a transposing B flat instrument. In other words, if you write for baritone or euphonium in treble clef, you must transpose the part, writing it a major ninth (an octave plus a whole step) higher than you want it to sound. Such treble clef parts were originally written for trumpet players who doubled on euphonium, to spare them from having to learn different fingerings. Many baritone and euphonium players will be comfortable reading either type of part, but, to be safe, you may want to provide each baritone or euphonium part both as a bass clef and as a treble clef part. If you are writing for a specific group, you may want to check on preferences.
These instruments have about the same range as trombones, but a mellower timbre. Like most lower brass, they are not as agile at fast notes as trumpets and woodwinds, but they can generally play extended passages of quick notes more easily than a trombone or tuba. They can also slur notes more smoothly than trombones and they have a clearer, more focussed sound than a tuba in the upper register. Considering their sweet sound and relative agility compared to other low brass, these instruments have definitely been underutilized, even by modern composers.
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