According to Patricia Crone in The Nativist Prophets of Early Islamic Iran, the difference lay in the fact that the Arabs captured the Sassanian capital and failed to capture the Byzantine capital. Ctesiphon was located on the floodplains of Mesopotamia and the Arabs were able to capture it early in their conquests. Constantinople, in contrast, is located in an easily defensible position. The Arabs besieged the city twice in 674 and 717 CE and failed in both instances to capture it.

I don't think the difference was due to "fighting ability" between the Byzantines and Sassanian Iran. The Sassanian general Shahin reached the walls of Constantinople in 615. The Arabs repeatedly conquered and reconquered much of Anatolia but, without Constantinople, they were not able to hold on to their gains, a fact due more to Anatolian climate and terrain rather than Byzantine military capabilities. Anatolia would have to wait until the Turks for the region to be Islamized.