The Napoleonic War profoundly changed the way Russians regarded their own country. Victory over Napoleon, not only in Russia itself, but all the way to Paris, strengthened Russia's sense of its own greatness as an empire and great power.
Many Russians, including some in the government, possibly even President Medvedev himself, would like to see Russia become a more Western country. The neo-Slavophiles do have quite a lot in common with Communists, who emphasize that Russia is different from Western civilizations.
The principal obstacle to a non-visa regime is that in Europe trust in Russia is at a low level, and what worries European nations is that criminals will come from Russia, or drug traders, or even terrorists. And therefore British and European governments want the opportunity to investigate each traveller before they come, hence the need for a visa regime.