What are the differences in treating patients as an md or do in emergency medicine?

None: Generally speaking allopathic(md) and osteopathic(do) training are similar and licensing boards, hospitals etc, recognize them as being so. Personally speaking one of my friends in undergrad whent to osteopathic while i was in allopathic and his training was great. Both become doctors. It is the further training/dedication/committment that makes the quality of the doctor, not their md v do degre.

Virtually None: The added ability to offer osteopathic manipulation is the hallmark of do education. In the average emergency practice this may offer added advantage in the fast track/urgent acuity patients. Otherwise, the training is all based on residency and practice experience which is equivalent for md/dos.