I think that everything that's in print is available on the web site, but there are also web-only things, so the print magazine may be a bit of a "quality/triviality filter" in that regard.
I like The Atlantic in general, although I think they have a bit of what I sometimes call a "contrarian bias", e.g., prioritizing "the conventional wisdom is X, but here's why it's wrong" think-pieces even when their theses aren't particularly strong. (Slate and Salon were much worse about that in their heyday.)
No, there is a lot of online-only content. I believe there's a daily email with new content, and often that content is quite weak compared to what's in the print version.
I would definitely appreciate a quality/triviality filter though, maybe the print is the only way to get it.