I have seen only one Vuillaume. It was nearly identical to a George Gemunder that I have seen and played. I also know a Derazey Bass that is a Vuillaume model as it was Derazey who also made Basses for JB. The brother you refer to of JB is Nicholas, correct? N.F. Vuillaume moved to Brussels (Bruxelles) who later employed G. Mougenot of whom
I have a Bass made the same year he took over the Shop of NF Vuillaume in Belgium. This bass I have looks just like a Vuillaume as well. On the Bernadel mention, which one is it, father or one of the sons? I also once owned a beautiful Bass by Gustave Bernadel c.1859. The Shoulders of all the Bernadel's I have seen are slightly more sloped than those of the Claudot's and Jacquet's as well as the makers of Vuillaume.
I do not know for sure if Mougenot was ever a maker for Vuillaume either directly or thru N.F but the model is nearly the same. On the graduations, I have never heard that 6mm# of Vuillaume but did hear that of Panormo. Perhaps if true, Vuillaume followed Panormo on the gauging.
The general complaints about these French models but not all of them are that the Shoulders are hard to get over, the string lengths often long, the 'stop' is long and the sound is often nasal as compared to other large basses. 'That French sound' is often spoken from people listening or playing many of these basses. Then again, 'that Italian sound' that English sound' and 'that German sound' is often mentioned once the players know the origin of the bass. Maybe they think it's just something to say to sound smart or maybe in some cases the generic national sound they hear is true.
I would love to see pictures of both this Vuillaume and the Bernadel you speak of. In the Elgar book there are two Bernadel Pere' basses listed. One one of them (p.139) you can see with a magnifier that the upper back has a purfled design like the factory basses with Pfretzschner and Morelli labels have along with some other German productions. I suspect that bass to be German and not French. Perhaps just one more error that Elgar has published.