How to Play the Tuba
How to Play the Euphonium
Tube thickness and pitch
Although there are thin and thick-tubed euphoniums, tube thickness does not affect the instrument's pitch. Mouthpieces, however, differ based on the tube thickness and they affect the pitch.
Also, most thick-tubed euphoniums have four pistons, but if they have three pistons, part of the tonal range in the lower register (when you use 1+3 or 1+2+3 fingerings) tends to sound sharp. Yamaha's YEP-321 and other models have thin tubes but four pistons, so they produce correct pitch.