It's strange, because I find many of the classic, romantic novelistic components of W&P--particularly the melodramatic relationship of Natasha and Prince Andrei--completely absorbing, but I'm now wondering whether I'd like them a lot less if they weren't combined with sweeping battle scenes, historiographic philosophy, and the fantastically entertaining skewering of Napoleon and "great men" more generally.
Because now that I think of it, I don't really care much about most of the characters in War & Peace; I suppose I like Pierre, and Andrei is admirable in his way, but the girls and women are not really believable, and most of the other men are just types. Similarly, in Anna K, I found Levin and (to a lesser degree) Vronsky interesting, but most of the others--including the title character--did not strike me as having meaningful interior lives. So while the plot engaged me, I rarely found it psychologically deep, except when Levin was on the scene.
And oh, that denouement! [QUASI-SPOILER FOLLOWS] The end of Book VII was just not at all meaningful to me. Sure, it was sad, but it didn't mean anything, and I think this is directly attributable to Anna K's weakness as a character. And everything that followed was just kind of blah. Similarly, I happen to like the end of W&P--you've gotta have a heart of stone not to love a 40-page essay on historiography!--but it is kind of a weird way to end that book.
Which brings me back to my intro, and also to the picture that accompanies this post, which depicts another great Russian who didn't quite know how to finish what he started.