Funny, I'm just reading War and Peace myself (the Anthony Briggs translation) and having the same reaction, gushing occasionally to people I know how approachable it is, and how darkly funny and modern it feels. Well, at least after passing through the first ~200 pages which are a slog. I didn't find even Tolstoy's historical musings boring, although he tends to repeat himself. And I usually suck at names, but the main characters are done so well I find them easy to remember. There aren't that many important ones despite how it seems at the start. It also serves as a fascinating peek into the daily lives of Russians of all stripes in the early 1800s.

I also had the same reaction to Crime and Punishment as the OP did.