Short story - I've been shooting w/ a 5d classic for around the past 4 years. I skipped upgrading to the 5d mk ii as other than resolution there were not enough differences for me to justify splashing out on the newer body. Now, I'm not going to get into the feature set too deeply - but the mkiii offers a substantial upgrade to 5dc users - af system, high iso performance, video, focus adjust, an many more.
That being said, I'm struggling with the lens before body advice! I'm using 17-40 / 50 / 70-200 now, and I could add some very nice glass or sell the classic and get the iii. I'd likely rebuy the 35l and 135l, but damn that mkiii is tempting for my work - mainly consists of shooting my baby, stock, and landscapes. Am I crazy to put body before lens just this once?