Well I can speak only for the Byzantine centuries here and we will start with Nicaea in 325.

Armenia was the first state to convert to Christianity even before Constantine. They were led by their king but the actual institution of kingship was dissolved not by Rome but by the Armenian Princes requesting as such from the Persian Shah in 428.

The actual land of Armenia in the Caucasus is highly isolated. Mountains, narrow passes and occasional open land made it defensible but poor for communication and raising large quantities of manpower. The Princes of Ani, Vaspurukhan, Tao, Lori and more were courted each in turn by Constantinople as allies against first the Sassanids and then Islam because they could be common Christian allies.

There was a problem though. Armenian delegations had never been present at the Fourth Ecumenical Council of Chalcedon in 451 as they were being invaded by the Sassanids (in a war to suppress Christianity) and they were uneasy about the division of Christ's Nature's into human and divine. It turned out that Byzantine and Orthodox theology were Orthodox with each other as a miaphysite agreement but all the recommunications that were declared failed quickly as Armenian Church practice was a little different too, use of unleavened bread and that sort of thing. So byzantium made use of armenian allies but they were not the utmost priority given that several Princes would ally with the Islamic powers even 30 years after Muhammad's death. (See Sebeos for this). Many individuals and families emigrated from the country for gold and military glory leading imperial armies but they did not often return and instead Byzantinised. (Charanis -Armenians in the Byzantine Empire)

So Armenia was a tug of war frontier period from 600-1050 until the Turks turned up. Later Byzantine practice from 960 was to have Armenian Lords bequeath their land to the empire but during the reign of Constantine X Doukas the armies failed and Armenia was demilitarised. Debate still wages over why and what (See Kaldellis Rivers of Blood). Armenia when it was reconstituted in Cilicia was a regional power but again limited to mountains in the Taurus.

Armenia in the late antique and medieval periods was sandwiched. It had defensibility but was not a region to control the Anatolian Plateau from and this meant that with the exception of (sometime) Armenian Edessa, wealth did not flood the Caucasus and it was a theatre of war for other, larger powers.