In terms of sound, I think that a muted bass trombone provides a much closer match to a bassoon (and the intended sound in most passages) than a euphonium with or without mute -- and this is particularly true for notes of short duration. I think that with regard to a euphonium, it's just not going to sound much like a bassoon whether or not you use a mute, and so I'd give up on the idea of that and just play it muteless. But I think that the bass trombone playing it muted would sound better. This is not similarly true for filling in for a bass or contra-whatever clarinet where I think the (unmuted) euphonium is a reasonable choice.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)