Rissian writers write with WARMTH
Russian literature is my favourite literature, as well. I think the reason a lot of people like it is because Russian writers describe their characters with so much sympathy, insight and love. There is a lot of warmth and humanity in most Russian works--particularly the 19th century ones---be it in the character development, in the description of scenes and nature, or the philosophizing which makes you feel as if you're reading about real life and living it in the moment that it's happening, rather than post-factum, "remembered" descriptions.
Tolstoy is a great master of this technique, and it's also interesting that while being very realistic in his descriptions and character development, he's also great at poeticizing the situations which imbibe them with more importance and meaning. That, I think, is also a characteristic of most Russian works---the simplest event or character is presented as very unique or special and, in turn, memorable.
This particular technique is what makes a big difference between works like "Anna Karenina" and "Madame Bovary". Although the intrigue and the situations are similar, the character of Anna Karenina creates the impression of a multi-dimensional, flesh-and-blood individual, whereas Emma Bovary lacks to a great degree individuality and uniqueness. The whole work of "Anna Kareinina" sparkles, despite the tragedy of its heroine, whereas " Madame Bovary" , although detailed and insightful, is a somewhat dull and pessimistic work.