I can certainly see that the Islamic forces would have been highly motivated compared to some of their opponents, but I'm not aware of any obvious military superiority.
The Roman Republic usually had superior organization and equipment. Various steppe peoples exploited mobility and the superiority of the horse archer. The Macedonians had revolutionary tactics, and were professionals facing mainly levies.
What was the Arab advantage over the byzantines, sassanids and others, aside from their former two having worn each other down?
I've written on this before, largely arguing that there wasn't anything particular special about the Arabs, except perhaps their quality of leadership and their approach to dealing with their defeated enemies. Another useful answer is this, in which I explained that it had always been Arab clients of the Romans/Persians who defended their desert frontiers, and that the two imperial capitals' neglect of these chiefs' interests had led to the initial losses during the Arab conquests. You might also be interested in textandtrowel's answer on why the Arab conquests were perhaps less 'Islamic' than you think, so the view that the Arabs had better morale due to their faith is highly debatable.