(I have both those lenses and love 'em both.)
When handheld, is it possible that the heavier lens could be steadier? I've always thought that to be the case for me. I'm much more prone to inadvertent motions when using lightweight gear. This is because I have never successfully been able to stop my heart beating while shooting and I can
sometimes see/feel the beats in my hands. On those days, the tripod is a must.
But of course, everyone's MMV on this.
So, yes, it would be interesting to see a follow-up comparison on-tripod.
And a question -- was the VR engaged on either lens? Sometimes that darned VR can cause more vibes than it prevents.
Also, the D800 has 36MP and the D600has 24MP. Do you think that the 36MP can be a factor in catching motion blur? I've convinced myself that I cannot handhold 36MP at all while I think I might be able to manage 24MP. (Prolly just kidding myself!)(((I really really hate tripods.)))
Meanwhile, I'm enjoying this nice snowy mountain scene.
Added later: It would be interesting to put the 70-200/4 on the D600 and the 200-500 on the D800??