FCP 7 was dominant but the disaster of early versions of FCP X forced a bunch of shops to switch to Premiere.
There are still things that make Premiere better. Recently I couldn't get an mp4 from a Sony cam to play at the right speed in FCP no matter what I tried, and it just worked in Premiere. I'm more fluid in FCP but I will probably switch too as Premiere just "feels more pro" now to me.
I've heard some great reports about Davinci, especially for post.
Most big-budget feature films are cut on Avid and that's been the case for a while now; for indies my impression is that it's 50/50 Premiere and Resolve, yup.