I've owned both lenses. They are both excellent, but they are also very different. If I had to buy one again tomorrow, I'd get the 300/2.8.
I think you're first going to have to decide which body your shooting although I think the D800 even in crop mode has more pixels than the D300.
For static wildlife (animals), I prefer the 300/2.8 with the 1.4 TC when using a DX body. For 95% of your shooting situations, this will be enough. The 300/2.8 + 1.4 TC is a razor sharp combination, even wide open.
I am not a birder, but as any bird photographer will tell you, the more reach the better. A 200-400mm with a 2x TC will give you more reach than a 300mm with a 2x TC... all day, every day You need to decide whether that extra loss of light will be a detriment to the type of photography that you do. There are other non-Nikon options, but keeping it in the Nikon camp, what about the 400mm f/2.8? Again, a very sharp combination when used with a TC.
It's obviously not hand holdable, at least for any length of time, but maybe something to consider.