In about 1843, Hector Berlioz wrote in his famous Treatise on Instrumentation "The bass tuba possesses an immense advantage over all other low wind instruments. Its quality of tone, incomparably more noble than that of ophicleide, bombardons, and serpents, has something of the vibration of the timbre of trombones. It has less agility than the ophicleides; but it's sonority is more powerful than theirs, and its low compass is the largest existing in the orchestra."
Berlioz wrote almost exclusively for ophicleide, as this was the primary bass voice instrument of the brass family in France at that time. The tuba had only existed for about 8 years (the Wieprecht/Moritz patent was filed in 1835) when he wrote the Treatise, and the entry on bass tuba was included almost as an afterthought; he wrote more words about the bass ophicleide than he did about tubas. There is little doubt that after hearing the tuba for the first time on a visit to Germany in 1842(ish), he liked the sound of the tuba.
But stories about him instructing his publisher to change the instrument title on his ophicleide parts are apocryphal at best.
Berlioz also referred to another instrument in his treatise called the bombardon which is roughly equivalent to the baritone horn, and the predecessor to the modern euphonium. Though rarely used in the orchestra, it was a popular brass band instrument.
In my scoring, I do not make the distinction between contrabass and bass tuba*, leaving this decision to the player. I also write for the euphonium (not baritone), and treat it both as a tenor tuba and as a lovely, warm tenor/baritone melodic voice. It is also capable of great technical virtuosity.
As I have discussed, the two main distinctions between Boulder Brass instrumentation and that of the Philip Jones Brass Ensemble are: 1) the use of a 2nd horn; and 2) the use of euphonium, occasionally assigned to play trombone. The PJBE philosophy is perhaps the converse of this - four trombones, with one occasionally doubling on euphonium. I will say that when we started out in 1993, we definitely leaned more towards four trombones with one doubling euphonium simply because that represented the instrumentation of the majority of music available to us.
But as more charts were written specifically for us, and I warmed up to the role of the euphonium in our group, that philosophy shifted. If one were to examine the totality of the writing for the Boulder Brass, you would perhaps see the most evolution in the euphonium writing - I now view it is an equal partner in all things, not only to the tuba, but also to the trombones, horns, flugelhorn, and solo voices in the trumpets.
*I have played both in the Boulder Brass and each brings something to the table. My preference is the excellent 822 F tuba by Yamaha, because it has the agility and ease of production in higher ranges, but is also a large enough instrument to provide weight in the bottom voice without over powering the ensemble. Nevertheless, the recording above was made on a B&S PT6 CC tuba. For Bolder Baroque, I played the 822, but also split the tuba responsibilities with then principal tuba of the Colorado Symphony, Walt Zeschin. Walt played a 5/4 Rudy Meinl CC on that recording.