I've had versions of both, in multiple calibers. They both shoot well. Neither are a skinny stainless tube. I think the smallest contour you can get in the Bart is a 2B. I don't know about Brux; the one I have right now is a 3. Rifling is different (5R vs 4 groove), but that's a wash.
If you don't mind the heft and you only wanted one or the other I would get the one with the shorter wait or less cost.
