First, communists in Russia still enjoy quite a bit of popular support - they continuosly get ~15-17% of votes in presidential election, and about the same percentage of parliamentary seats. Compare that, for example, to Ukraine (3.8% votes in 2014 parliamentary elections and 1.5% in same year presidential election) or Poland (no representation in Parliament).
Second, quite a bit of Soviet statuary actually were taken down in Russia. Also, some objects named for communist figures were renamed, even some cities. But demolishing statues and renaming streets (or rebranding "militsiya" to "police") costs money, and with economic situation like it was in Russia during the 90s, it probably seemed inappropriate to waste funds on such non-essential tasks. Moreover, Russian government in the 90s made a big point of Russian Federation being the legal successor to the USSR. That would clash a bit with attempts to destroy the legacy of that regime. Other post-USSR countries, on the other hand, were founded on nationalist ideals, and their governments were quite committed to distancing themselves as far from their past as possible, so destroying statues was an important action to them and their electorate, and expenses were more justified in their eyes.