I don't agree with this. Dostoevsky's characters are philosophical archetypes, vehicles to express particular views or psychological states he wanted to explore. Tolstoy's characters are not such representations of ideas, but actual rounded human beings.
If you come away from reading The Idiot thinking "wow, what a tiresome, failed philosopher", with all of its multi-page mouthpiece rants from characters about how the Roman Catholic Church is evil or whatever, I can understand that. If you think the same after reading Anna Karenina, I don't really know what to say.
You too have it backwards. That's exactly what I come away with from
Anna Karenina, and also what his acolytes came away with. Constantine Levin is a tiresome cardboard cutout for Tolstoy's ideal agrarian aristocrat. Have you not heard of the Tolstoyan movement? Dostoyevsky doesn't have a comparable movement because, unlike Tolstoy, he wasn't an ideologue. And since you've brought up
AK and
The Idiot, compare Kitty Shcherbatsky with Natasha Filipovna and tell me which is a lifelike portrait. Do the same for Rogozhin and Vronsky. Who is more vivid? Dostoyevsky created characters obsessed with ideas but usually not his own ideas. Dostoyevsky's novels are renowned for the independence of his characters' voices and the indeterminacy of their motivations from an authorial perspective. I refer you to critics Philip Rhav, Leonid Grossman, and especially Mikhail Bakhtin on these points.
As for religious rants: You are aware that anti-papist, anti-RCC sentiments were widely held in Russia when Dostoyevsky was writing and it makes perfect sense that some of his characters took up these ideas, right? Ivan Karamazov's brilliant poetic essay, "The Grand Inquisitor," is a prime example. Even in that case it's not certain how invested Ivan really is in these ideas, let alone Dostoyevsky. The ideas are just aspects of characterization, not ideas the author is pushing.