I have not had a chance to do such a test. But based on tuba experience, I'd expect the differences you'd see would be:
- The degree of "projection" of the sound -- particularly noticeable in large halls or outdoors. A larger bore and a larger bell just pitches sound better.
- The "gravitas" of the sound -- which means, basically, richness in the low range.
- The ease of playing (articulation, speed, sound quality, and effort) in the contra bass range, and particularly in the compensating register. With a compensating instrument, bore size starts to really matter in that range because of the extra tubing involving and resulting pressure resistance.
- The ease and tone quality in the high range (above the staff). This is where the smaller horn really sings and the larger one loses focus.
- Feeling of confidence and satisfaction -- and effort -- in supporting a large ensemble if you're the ONLY tuba. Even with the Champion, doing this in a 45+ member community band is taxing. If you have one other section mate (with a CC or BBb horn, preferably), life is much better. But with the smaller horn, it's even more difficult to hold up that end of the ensemble by yourself.
- By the same token, in small ensembles (quintets, etc.), the smaller horn can work and fit in better.
All of these involve trade-offs, and none should deter you. I think I'd not want to be the tuba in an orchestra with the Solo or the Bombino, but I'd go for pretty much anything else.
Mouthpiece makes a difference. For me the Wick 3XL is just absolutely the best, hands down. If you get a chance, try one. The Wick mouthpieces are particularly well suited for these Eb British-style horns -- and were in fact designed for them. Wessex used to include a Wick (generally a 2L, I think) with their horns, but I believe went in a different direction, I would guess, as a cost-cutting/profit margin move. As a trombone player, I believe you'd find the 2 size a bit big. For me, it's a little too big -- but sometimes I shift to it for special occasions (some Wagner, Sousa, etc.). It takes all the air I've got, but produces BBb-like performance in the contra range. And I lose the focus and singing quality above the staff.
Be sure you go to one or more Tuba Christmas events this year, and have a really good time.
One other thing ... I find that if I switch back and forth between bass trombone and tuba, it takes me a while (and I mean more than a few minutes) to lock back into hitting the pitches and right partials. When I committed to really learning bass trombone this past year, I just put the tuba away and didn't touch it. You may experience the same problem. Just be aware that it may take a bit of effort to do those switches happily. If I had to (e.g., in something like a pit orchestra) switch back in forth during a performance, I could do it -- but I wouldn't be at all happy with my sound/performance on either instrument. But maybe that's just a comment on my own skill.