I've only seen three films in 3D so far: Avatar, Alice in Wonderland and How to Train Your Dragon.
With the exception of Alice, I've also seen them on the big screen in 2D. Out of those three films, How to Train Your Dragon was the only one which I felt had consistent and genuinely immersive 3D. It was also the only entirely CGI flick of the three, which may also be a factor. No darkening, no flickering, no awkward 'carboard cutouts placed at different distances from the screen' effects.
Still, of the films whcih I've seen in both formats, neither lost anything when seen in 2 dimensions rather than 3. If anything, Avatar worked a little better for me on a flat screen.