It's an interesting question.
There are three major Christian nations in Caucasus: Armenians, Georgians and Osetins.
Armenians got their independance in 1992 together with other 14 republics. In 92-93 they had a war with Azerbaijan and won it with assistance from Russia and Iran. Azerbaijan was supported by Turkey, an important NATO member.
Armenian population really suffered in Azerbaijan since 1988. In Jan. 1990 there Armenians were slaughtered in Baku, those who were lucky had to literately run away. Gorby was so kind that he waited for several days to send troops to restore order, waited until there were almost no Armenians left in Baku. Before 1990 Armenians were the second national diaspora in Baku...
Georgia also got intependant in 1992. Their almost-insane nationaly elected president Gamsahurdia started a civil war, and later was overthrown and killed. Old Soviet leader, former USSR Foreign minister Shevardnadze came back to power. At that time three autonomies inside Georgia declared independance: Ajaria didn't start military struggle, but Moslim Abkhazia and Christian Southern Osetia had full-scale war to protect their "independance".
Chechen troops first saw combat and were the main military power on Abkhazian side in 1993. Yeltsin armed Chechens to make them a "sword of Damocles" over Caucasus, but then they went out of control and started genocide against non-Chechen population in their own "republic". Abkhazian war resulted in thousands of Georgian refugees, many people were thrown out of their homes and moved to Georgia and Russia... Russian government almost openly supported Moslim Abkhazians against Christian Georgians there.
Osetia was divided in two parts during Soviet times. Northern Osetia is a part of Russian Federation, Southern - a part of Georgia.
There are Russian peacekeeping forces both in Abkhazia and Southern Osetia. New Georgian president, pro-American Saakashvili is definetly mentaly disabled. He ordered to open fire at the ships that bring Russian tourists to Abkhazian natural resorts... He also provocates hostilities in Southern Osetia. BTW, this time Chechens fight on Georgian side against Osetins. It's obvious, because Georgia hosted their bases in Pankisi Gorge and provided all kinds of assistance to terrorsits. At the same time mr. Rumsfeld stated that US will fight any attempt to threaten Georgia when Russia demanded to stop supporting Chechens

The reason for this two nations to fight for independance was general situation in Georgia, proably the worst among all former Soviet republics. Their inflation rates beat all records, income per capita is not enough even for bread

Now 70-90% of Southern Osetians and Abkhazians have Russian citizenship, they pray on Russian tourists and don't want Georgians to spoil their business.
Caucasian diasporas in Russia are very big. It seems to me that over 50% of Georgian males drive private taxi-cabs in Moscow. Armenians hold shops and Azerbaijanians control market trade. Georgians and Armenians working in Russia produce maybe more then 50% of their countries national income.
I don't pretend to give you a complete picture and have to admit that I may be biased.
BTW, Fariz is from Baku, it should be usefull to ask him about this affairs.
What you saw about Russian security forces mistreating Caucasians is not an official policy. For our beloved Militia dark-skinned big-nose unshaved people are a great source of money. After every terrorist act they start fishing for Caucasians and leeching money from them.
When I say "Caucasian" I mean a person from Caucasus, dark skin, big nose and special accent, not any person belonging to European race. It's not bigotry, it's just a copy of an official term used by Militia: "a person of Caucasian nationality".
As for me - I really enjoy this people living here in Moscow. They are great salesmen, always polite and friendly.