If you do a search on the web, you will find plenty of articles which point to cheap labour in Dubai (these are general and not specifically related to Emirates), however, I would be very surprised if one of the main factors in their success was the relatively low costs of using Dubai airport.

Additionally, as Dubai is their base, and doubtless they have staff based in other cities around the world, they are going to benefit from more cost effective routes transiting their own country, just as SQ, CX and other Asian and Middle Eastern carriers will.

BA and LH probably have the edge if you are flying from the Middle East to anywhere in America (perhaps with the exception of New York, but even then BA or LH may be more competitively priced). But flying to Asia Pacific from Europe, EK is bound to be able to be so competitive, because its frequencies, and as I mentioned the relatively low costs at Dubai (I stand to be corrected as far as Dubai is concerned, but I can't believe that EK is paying a lot to use this airport).