My husband's Sigma is the new model, it is 5/6-6.3 APO HSM with OS. He bought it approx. 12-18 months ago. I have it out to try on my D800, but it is cloudy and windy, not a good day for shooting. Still, I may go out for a bit today with it.
I only put the 80-400 on the D800 about twice. Set up on my patio with a monopod, which is what I've done for years shooting my backyard birds. I have a crabapple tree about 10 feet off the patio and it is great for staging. With my DX cameras, I could pretty much fill the frame with a bird, leaving some background. I often got excellent results, even with my D7000 which was a nice jump in mp from the D300.
The images I took with the new camera and 80-400 were blurry, OOF a lot of the time, and just basically bad in comparison. The lens seemed very slow to focus on the D800 compared to the D7000. Slow focus is bad when you are birding. Plus I really noticed the lesser reach. One thing I haven't tried yet is to use that combo in DX mode. I plan on trying that and seeing if IQ improves, but heck, I'll lose the large file size. Still an option.
So now what I need to do is try the 80-400 again with better technique, then try it in DX mode. Then shoot with the Sigma and compare.