Julia's had the name and reputation, but Morphy bought them out. So by acqusition, Morphy's is now the big dog.
Other than really high end guns, though, I really cant see the benefit of an auction house over Gunsinternational. And the reason isnt the price, or even the pictures.
It's because you cannot solid answers to questions.
I have inquired to several auction houses over the years with questions. Answers, if I got them, were never timely or particularly informative. I dont see any auction house really overcoming this if you cant go and be there. Almost no one who isn't retired has time for that.