The primary pushers of this movement are nationalists and regionalists. Organizations like the Russian Orthodox Church have redeemed the Imperial Age in the eyes of the people. The corruption of the Tsars is ignored while the focus is shifted to Russia's dual nature as a continuation of Rome/Byzantium while being uniquely Eurasian. Nationalists compare this vision of the past to the imposed universalist vision of the Soviet Union. Regionalists have also made peace with popular culture by emphasizing their own region's culture as part of the salad bowl which is the Russian Federation.
Meanwhile, in the former Soviet Union national states like Ukraine, Estonia, and Georgia (the Near Abroad) the opposite is occurring. Ethnic Russians and their allies are the ones who feel they are losing out from the cultural landscape changes. High levels of nationalism by the post-Soviet states have caused many ethnic Russians to have nostalgia for the Soviet past where Russia and everything Russian was "first among equals." Ethnic Russian cities in Ukraine celebrate "Red Army and Navy Day" instead "Defender of the Fatherland Day." Ethnic Russians in Estonia riot when the Estonian government removes a statue of a Red Army solider from the main square.
The biggest landscape battle though to restore the old Soviet mindset is in the breakaway Georgian republic of South Ossetia. The city of Akhalgori was in the former Soviet Georgian oblast of South Ossetia. When Georgia was becoming independent the city was transferred out of the region. South Ossetian rebels claimed it as part of their country but where unable to take the majority-Georgian but mixed city. However, in the 2008 war the city was taken by a combined force of Russian and South Ossetian forces.
Ossetians see themselves as a smaller but equal partner to Russians. I once attended a fascinating lecture on Ossetians which describes how they see themselves as a younger brother to the Russians. Throughout history this has played with Ossetia eagerly joining the Russian Empire, supporting the Soviet Union during World War II when the Germans were recruiting minorities, and by staying in the Russian federation after the USSR's collapse. Monuments and memorials in North and South Ossetia demonstrate this relationship as well. Today the South Ossetian government continues the relationship by calling Akhalgori by its Soviet Name, Leningori.
The reason for this phenomenon is fairly straight forward. In what I call the Rule of Nationalism distance decay is reversed. Nationalism becomes more intense along the frontiers and away from the hubs. Ethnic Russians and their allies outside of the Russian Federation feel threatened by encroaching cultures. Inside Russia, Russian culture is not threatened so people seek to identify themselves via regionalism. People like the President of Chechnya and Tatarstan have managed to hold onto power by playing up regionalism while pledging loyalty to the Kremlin. This has prevented regionalism in Russia from threatening Moscow and has allowed regionalism to bloom in the Putin era.