I have always associated Browning with obvious quality. The fit and finish are top notch at least in my observation. I can't recall ever seeing anything less than beautiful blueing, wood, ect.
Why there seem to be no Brownings in long range competition. I don't see any obvious mechanical attribute that would make it more suitable as a starting point for competition.
The receiver is, like almost all other modern designs on the market, drilled bar stock. Three lug bolt, is becoming very popular now days, my Cooper rifle has this design too, along with Sako, and several other custom makers. 60 degree lift along with there being less removed for lug recesses make this attractive but requires more machining.
It would seem to me that there are easier starting places for long range competition. Kind of like making a Lincoln a rally car.