I've seen just about everything brosing side by side with deer. White tails are deffinitely not one's to play well with others when in the rut, as are moose, elk, and antelope. But I think it's safe to say that a moose will take charge in any of the above circumstances, with elk placing second.
Although this isn't really relevant to your question, I do know that white tail deer will breed a mule deer, and they dominate in that way. Out here in Arizona we have the little couse white tail which is only about 65 - 100 lbs. max, but just because they are little doesn't keep them from dominating and cross breeding mule deer weighing twice as much. We have a lot of hybrid mule deer out here that have distick white tail racks as a result.
GS