the problem is that the Church universally used leavened bread. Understood correctly, I don't think the difference is a problem.
The great problem with unleaved bread is that the Church first encountered it as a phenomenon of heresy. It was adopted by the Armenians as a way to asssert that Christ has only one nature. So when the Churches of the East come upon unleavened bread in the Eucharist ancient warning signals go off for them...
Something interesting from Fr John H Erickson, Dean of Saint Vladimir's Seminaryhttp://www.svots.edu/Faculty/John-Erickson/articles/beyond-dialogue.html/
"...... Particularly instructive are the ways in which certain distinctive Armenian liturgical practices, such as the use of azymes (unleavened bread) and a chalice unmixed with water in the eucharist, come to be linked to Christological doctrine. The origins of these practices are unknown, but they certainly antedate any division of the churches. By late sixth century, however, they were becoming symbols of Armenian identity vis-a-vis the Greeks, who used leavened bread and wine mixed with warm water in the eucharist.
"Refusing an invitation from Emperor Maurice to come to Constantinople to discuss reunion, Catholicos Movses II in 591 declared: “I will not cross the River Azat nor will I eat the baked bread of the Greeks or drink their hot water.” 
"By the late seventh century these distinctive liturgical practices, already symbols of national identity, have become even more potent symbols of Christological doctrine. Reflecting the aphthartodocetism of Julian of Halicarnassus, which was then in the ascendency in the Armenian Church, Catholicos Sahak III (d. 703) writes: “Now we profess the body of Christ [to be] incorrupt and all-powerful always and constantly from [the moment of] the union of the Logos. This is why we take azymes [unleavened bread] for the bread of holiness with which we offer the salvific sacrifice, which signifies incorruptibility.”  Then, after a barrage of typological and moral arguments supporting the use of unleavened bread, Sahak goes on in like manner to associate the unmixed chalice, free from the adulteration of added water, with the incorruptible blood of Christ.
"The Byzantine Church quickly enough responded in kind. The Synod in Trullo (691-92) almost certainly had Sahak’s treatise in mind when it decreed that any bishop or presbyter who does not mix water with the wine in the eucharist is to be deposed, on the grounds that he thus “proclaims the mystery incompletely and tampers with tradition” (canon 32).  Very possibly Trullo also had Armenian liturgical practice in mind when it decreed “Let no man eat the unleavened bread of the Jews...” (canon 11). In any case, in subsequent polemical literature the issue of the bread and wine of the eucharist figures prominently, frequently to the exclusion of deeper theological reflection.
"Thus, despite their common rejection of Chalcedon and the generally Severan orientation of their shared Christology, the Armenian and Syrian churches in the Middle Ages sometimes attacked each other precisely because of such liturgical differences. So also, as schism yawned between the Byzantine and Latin churches in the eleventh century, Byzantine polemicists transferred their anti-azyme arguments from the Armenians to the Latins, notwithstanding the latters’ manifestly Chalcedonian Christology. Use of leavened bread and mingled wine, or conversely of unleavened bread and pure wine, immediately marked a community as either heretic or orthodox, no matter what Christological doctrine the community in question actually held!"