It's not that Russian values overall are better than Western ones. I would argue Russian Orthodox values are more supported by the Russian population than Catholic or Protestant values are supported by Western European populations.
Progressivism is becoming the religion of Western Europe and even North America. The values put forward by this ideology are often very destructive. The Sexual Revolution, for example, negatively affected the family structure in the West and expedited the spread of venereal diseases.
Russia went through a lot of terrible things under the Soviet Union, but when it fell, the people responded by embracing the Russian Orthodox Church. The faith had never truly gone away, but under Soviet rule, Russian Orthodox Christians had to worship in secret for the most part. With Communism gone, they were now able to worship openly. This allowed Russian society to slowly get back in touch with its spiritual culture. We're seeing the opposite trend in much of Western Europe, as they embrace more materialism, progressivism, and secularism.
Ironically, however, the rise in Islam's presence may mean some significant changes for Western Europe in terms of culture. Migrants tend to be a lot more family-oriented and traditional than the native populations, and this may result in Islamic values taking hold in certain parts of Western and Northern Europe. It will be interesting to watch.