I haven't seen any reviews of the new Sigma 120-300 yet, but the Sigma seems a much more interesting lens to me due to the faster aperture (as long as it's sharp).
The difference between 300-400mm isn't that much, and I'd rather take the extra aperture latitude, and then if needed just use the lot's of MP's to crop to desired composition.
Beyond the big weight difference you are wrong about 300mm vs 400mm, it is very noticible for wildlife. My wildlife photography made a big jump going from 300mm to 420mm. 300mm on FF is too short for most wildlife, 400mm isn't even that long but very hard to do better without serious money.
Of course the sigma can take TCs so then it a question of IQ of a bare 80-400 vs a 120-300 with 1.4TC. The sigma combo can be stopped down 1 stop to match the slower nikkor and by then is probably similar IQ but at twice the weight.
For sur the sigma is nice but it doesn't compete with the 80-400 except you get more glass for your money which is tempting.