I looked at the New Cambridge History of Islam, It does not give a conclusive answer. It says that arabs probably had a better strategy and more will to fight. The christian lands were not properly defended and the empires were not interested in starting new wars. Here is an excerpt.

What explains the success of the early conquests? The size of the armies is impossible to measure with any accuracy. Some Christian sources, which are generally keen to exaggerate the catastrophe of the defeat, speak of extraordinary casualties: a contemporaneous Syriac account has 50,000 killed in a single battle in Syria; another early source, which was probably written some time in the 670s, has the Arabs kill no fewer than 100,000 Byzantines in Egypt.52 The figures given by the Islamic sources for the numbers of combatants are generally much more reasonable, often in the hundreds or low thousands; even a large army, such as the one that fought at al Qadisiyya, probably numbered no more than 10,000 or 12,000 men.53 These more modest armies, which would be much easier to provision and manage, make considerably more sense. Since there is no good evidence for any substantial reduction in Byzantine manpower (and virtually no evidence at all for Sasanian numbers, reduced or otherwise),54 it is probably safe to assume that Muslims were often outnumbered. Unlike their adversaries, however, Muslim armies were fast, agile, well coordinated and highly motivated. The speed of the conquests on both fronts as we have seen, the decisive battles took place in the space of four or five years also suggest that, whatever their numbers, both the Byzantine and Sasanian defences were brittle. In contrast to the large scale, resource intensive and protracted campaigns that were so typical of Byzantine Sasanian warfare of the sixth and early seventh centuries, and which in at least some places resulted in widespread violence and social dislocation,55 the Islamic conquests of the mid seventh century read like a series of relatively short engagements (the great battle of al Qadisiyya is said to have lasted three days), which were made by relatively small and hit and run armies that rarely laid sieges of any length or produced casualties in large numbers. In many and perhaps most cases in the Byzantine provinces, local elites cut deals that avoided large scale violence. Modern descriptions of systematic conquest era violence targeted at non Muslims, in addition to those of post conquest persecution before the Marwanids, are usually nothing more than poorly disguised polemics.56 If the historical tradition would have us infer that large scale mortality and dislocation were very occasionally the exception to a general rule, the archaeological evidence clinches this inference. Unlike the barbarian invasions of the fourth and fifth century western Mediterranean,57 the effects of the Islamic conquests were in many respects modest. There is a fair amount of regional variation, but there is no sure archaeological evidence for destruction or abrupt change in settlement patterns that we can directly associate with the events of the 640s and 650s. In Palestine and Syria, where rural settlement seems to have reached a peak in the middle or late sixth century, the conquests bore no impact upon a decline that had apparently begun before they took place.58 In Syria, we also know that transformations in urban space that earlier generations of historians had attributed to Muslim rule may have actually been under way before the Muslims arrived.59 Patterns of occupation and use in the towns of the northern Negev, to take an example that is particularly striking, seem to carry on through the seventh century with little appreciable change; the story changes in the course of the eighth and ninth centuries, when decline sets in, presumably accelerated by the shift of the caliphate to Iraq, although the earthquake of 747 had deleterious effects elsewhere.60 The evidence is very poor for Iraq, but there, too, archaeology suggests that conquest effects were far from catastrophic.61 Of course the shift of the caliphate from Syria to Iraq may have resulted at least in part from underlying economic changes, but precisely how the political history of the early caliphate relates to the economic history of the Near East remains unclear. It is certainly the case that locating the centre of the caliphate in Syria, which was enjoying an Indian summer of a flourishing eastern Mediterranean economy, initially made much more sense than doing so in or around the Gulf, which had apparently suffered several centuries of economic decline.62 In this connection it is noteworthy that the political frontier in northern Syria that would long separate Byzantium from the caliphate, unlike the political frontier that had separated Byzantium from the Sasanian empire, appears to coincide with an economic (and geographic) frontier that had separated Anatolia from Syria on the eve of the Islamic period. If the waves of conquest only reached as far as the highest tide of economy had reached earlier, one might think that economy and conquest were fairly closely related.63 Whatever the precise course of victory, to the victors went the spoils.

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Of course things were very different for non Muslims. Here the events of the conquests were typically assimilated into pre existing patterns of mono theistic history, and the agents of those conquests, the ‘Arabs’, ‘Saracens’ or ‘Hagarenes’, were assimilated into ready categories of monotheistic belief. In other words, the conquests were proof of God’s wrath, and Muslims were heretical monotheists. Put another way, although the deep syntax of historical explanation history is made as God operates through men was shared by all monotheist historians, whether Muslim or Christian, for non Muslim monotheists the events signalled a wrathful rather than a merciful God. As early as about 634, the patriarch of Jerusalem wrote of the ‘Saracens who, on account of our sins, have now risen up against us unexpectedly and ravage all with cruel and feral designs, with impious and godless audacity’. 69 Twenty or thirty years later, a chronicler in northern Mesopotamia asked: ‘How, otherwise, could naked men, riding without armour or shield, have been able to win, apart from divine aid, God having called them from the ends of the earth so as to destroy, by them, “a sinful kingdom” [i.e. Byzantium] and to bring low, through them, the proud spirit of the Persians?’ 70 Daniel’s apocalyptic vision proved especially accommodating to Christians struggling with the significance of the conquests and early Islamic rule. Thus Daniel conditions the words of an Armenian chronicler writing some time in the early 660s: ‘I shall describe the calamity which beset our time, the rupture of the vein of the old south and the blowing on us of the mortal hot wind which burned the great, leafy, beautiful, newly planted trees of the orchards. This [happened] rightly, because we sinned against the Lord and we angered the Holy One of Israel.’ 71