What is the difference between Georgian and Russian orthodox church dogmas?

Answer 1

The only difference as I see it, is not in the dogmas (that is, the teachings) but is historical.

Georgian Orthodox church has been autocephalous (self-governed) from the 5th century and they are proud to be one of the oldest Christian communities (from the 1st century) in the world. Georgia was evangelized by the Greeks and has strong ties to the church in Constantinople. Their liturgies stem from the Byzantine tradition, and their liturgical language remains an archaic Georgian.

From Wikipedia:
"In 1801 the Kingdom of Kartl-Kakheti Eastern Georgia was occupied and annexed by the Tsarist Russian Empire. In 1811, the autocephalous status of the Georgian Church was abolished by the Russian authorities, despite strong opposition in Georgia, and the Georgian Church was subjected to the synodical rule of the Russian Orthodox Church. The Georgian liturgy was suppressed and replaced with Russian.
Following the overthrow of the Tsar Nikolai II in March 1917, Georgia's bishops unilaterally restored the autocephaly of the Georgian Orthodox Church. These changes were not accepted by the Russian Orthodox Church or by the invading Soviets in 1921, who subjected the Georgian Orthodox Church to intense harassment. Hundreds of churches were closed by the government and hundreds of monks were killed during Stalin's purges. The independence of the Georgian Orthodox Church was finally recognised by the Russian Orthodox Church in 1943, but it was still subjected to constant pressure and attrition in the post-war anti-religious campaigns of the Soviet authorities.
In 1989 the Patriarch of Constantinople recognized and approved the Autocephaly of the Georgian Orthodox Church (which had in practice been exercised or at least claimed since the 5th century) as well as the Patriarchal honour of the Catholicos. Georgia's subsequent independence in 1991 saw a major revival in the fortunes of the Georgian Orthodox Church."
http://en.wikipedia.org/wiki/Georgian_Orthodox_and_Apostolic_Church

Answer 2

About 15 Rubles :-)