(This post is from an email conversation with a friend. I thought the content might be useful for others.)

I have two Nikkor 300/2.8 lenses, the VR I and the older AF-S Mk 1, and agree with everything Larry said.  I use the VR model all the time now and love the image quality (on D810 and D500), quick focus, and the relative ease of travel with it.  I have all three TCs and don’t hesitate to use the 1.4.  Sometimes I have to use the 2.0 and it’s acceptable when stopped down a bit.  You can (almost) never get close enough for birds.  I often use a monopod (the Gitzo 5561 rocks!) to ease the load and to shoot stationary birds, but all my BIFs are handheld even though I have a never-used gimbal head in the closet.  Another thing I like is the ability w/the TC2.0 to shoot macro (-ish) shots from 6-10 feet away.  Your subject doesn’t even know you’re there!
Here are a few 300/2.8 VR samples illustrating my points (EXIF included) (hand-held unless otherwise stated):

I sometimes wish I had the 500/4 Nikkor, as it is also hand-holdable, not much more difficult to travel with, and adds about 20% more reach for the same aperture.  It’s just hard to justify the expense.

As far as the 200-400/4 is concerned, I’ve never shot with one and regularly see them out birding.  It would be nice to be able to zoom out since it’s sometimes hard to find my subject when I bring the 300 w/TC up to my eye.  I’ve never seriously considered the lens, though, because although it is sharp closer in, it apparently doesn’t do well past 100m.  I’ve read Thom’s stuff for years and trust his opinion quite a bit.  (His book on the D500 is great, BTW.)  For birds that wouldn’t be an issue, but it would be for larger subjects farther away.

In lieu of a zoom capability in the lens, I did start taking advantage of a feature in the D810 when I was using it for birding before the D500 came out, and continue using it even with the D500.  When I’m in still photo mode I have the video record button (button with red dot by the shutter button) set to change the image area and easily switch from the normal image area to the smaller cropped area.  That turns the D810 into a 15MP DX format and the D500 into a 12MP 2.0 crop format.  Whenever I’m shooting something that I can’t get close enough to to fill the full image area, then this trick does a few nice things:  gives my 300 greater (apparent) reach, reduces the file size, speeds up the frame rate on the D810, and gives me a bit of the benefit of a zoom lens in that I can see more in the viewfinder around my active image area and have a better chance zeroing in on my subject.  Once you get used to it, you can easily switch back and forth nearly instantly and without taking your eye away from the viewfinder.

I had a Nikkor 300/4 in the past and loved it.  It was very sharp and very easily hand-holdable.  It was a great entry point, but I quickly ran into its limitations and moved to the 300/2.8 AF-S.  (And BTW, the move from the 300/4 to the 300/2.8 was a shocker with respect to hand-holding.  It is much much more difficult to do with the bigger lenses.)

Bottom line:  I highly recommend the Nikkor 300/2.8 (any model from AF-S on).