Their dedication to neither Boeing or Airbus. i know many other airlines have combined fleets if not all, but I believe Emirates have become so successful because of their openess to both companies markets. Because Emirates fly mostly medium haul flights the high capacity planes at this range include the 767ER, 777 all variants, the A330 and the A340.
Emirates' fleet currently consists of 777's, A330's and A340's. (A300 not included in this analysis) The big question when it comes to ordering planes of this size and range is 777 or A330? I believe by purchasing both of these planes and using them flexibaly, depending on which route requires it the most, Emirates have created themselves a very sucessful market that will continue it's sucess for many decades.
The next "step up" in model terms is A340 or 747? And although Emirates only currently has A340 for PAX ops, its does use 747's for cargo flights. And its high density flights will soon be taken over by the A380 and the A340's used on lower density routes.
So although Emirates seems to be a serious Airbus customer, the presence of 777's in it's fleet, depicts that it has kept its options open and kept the money flowing at all times.
Thoughts welcome, sorry for the essay
P.S or Emirates sucess could just be to do with Dubai's position as a major world hub