Apart from the obvious external form difference, how do a bass trumpet and a valve trombone differ?
There are a number of instruments in the pitch class of a trombone and each of them have interesting and unique features.
The Valve trombone bears the most resemblance to a slide trombone because in many cases, the valve section is interchangeable with the slide section to the extent that many of these models are sold with the valve section as an option. This includes :
The sound of the instrument is actually quite similar, mostly differing in the articulation. There is actually another instrument that combines both the slide and the valves called a "Superbone". For a long time, Holton was the only manufacturer but Wessex and Shagerl now have a model in current production. The demonstration video done by James Morrison is quite excellent. That link in particular will take you to a spot in the video where he demonstrates the advantages of one over the other by playing two licks: one that works well on the valves and one that works well on the slide utilizing both of the mechanisms in isolation and then in tandem.
Bass trumpet, in contrast, has a much more strident sound because they are often made to be the same bore size as a trumpet and share a similar profile. With a slide/valve trombone, half of the instrument is cylindrical, meaning there is virtually no taper from the leadpipe (the part immediately after the mouthpiece receiver) through the slide tenon (the part that connects the slide/valve section to the bell). With a bass trumpet, the leadpipe is directly attached to the valve section so there can be more overall conical tubing and the taper of it can be over a greater expanse. Additionally, the bells are much smaller than on trombones. The smallest of contemporary valve trombones has a bore size of around .485 and usually have a 7.5" - 9" bell flare. Compared to models of bass trumpet:
- Wessex's bass trumpet is .46" bore with a 6" bell
- Bach B166 has a .485" valve bore with 7" bell
- Joseph Lidl has a .460" valve bore and a "small" bell
- Kanstul 1088 has a .485" valve bore and 7" bell
- The Alexander 19 has a .492" valve bore and a 6.2" bell
- The Thein "New York" bass trumpet has a valve bore of .512" and a 6" bell
Note however, that not all of these bass trumpets are equal. Some have 3 valves, others have 4. Some are pitched in C and others are pitched in Bb. The C trumpets with 4 valves are more often used for orchestral work and the Bb ones sound more like the typical tenor trombone. The Kanstul goes even further and is very similar to a valve trombone because it has much more length of conical tubing before the valve section, leaving the portion after the valves similar to the bell section on a tenor trombone.
Finally, a hybrid between the valve trombone and the bass trumpet is often used by marching bands and can be called a "Flugabone" or a "Marching Trombone" depending on the manufacturer. (The terms can be used interchangeably.) Wessex and Kanstul currently have offerings in this category. They are similar in appearance to the now defunct Olds and Blessing "Marching Trombones". Unfortunately, King no longer sells their Flugabone and I can't find a picture of one that isn't from eBay. These are much more close to valve trombones than are bass trumpets because the valve bore are often the same or larger (the above models all have a .500 or .522 valve section) as well as a larger bell section (the above models all have an 8.5" bell).
Additionally, the amount of tapered tubing is much more similar to a trombone than to the bass trumpet due to the additional length of tubing that occurs between the leadpipe and the valves. E.g. a flugabone has a smaller distance between the valves and the end of the bell than a bass trumpet. It also has to go from .500 to 8.5". This means the taper is more rapid in the flugabone than it is a bass trumpet, which has a longer distance to get from .485 to 6".
According to those sources,
The bass trumpet is a type of low trumpet which was first developed during the 1820s in Germany. It is usually pitched in 8' C or 9' B♭ today, but is sometimes built in E♭ and is treated as a transposing instrument sounding either an octave, a sixth or a ninth lower than written, depending on the pitch of the instrument. Having valves and the same tubing length, the bass trumpet is quite similar to the valve trombone, although the bass trumpet has a harder, more metallic tone. Certain modern manufacturers offering 'valve trombones' and 'bass trumpets' use the same tubing, valves, and bell, in different configurations - in these cases the bass trumpet is virtually identical to the valve trombone.
Personally I find that disappointing, as I'd have hoped that "bass" trumpets kept the bore profile of the regular trumpet series, thus differing from the bore profile of trombones. That's life.