I remember all to vividly the pre-focussing on motorbikes days, and while teflon-mike's suggestions are valid, the OP has a nikon D3, which in itself should be more than capable of keeping the owl in focus given correct technique.
According to the exif, you were at iso 1600, and given the technical quality of the posted shot, I'm guessing that this is a fairly hefty crop. Normally a D3 wouldnt show this much noise with minimal cropping at iso 1600.
If I'm right (could be wrong), then I'd suggest you need to concentrate on filling the frame when shooting rather than cropping afterwards. In my opinion, this is what has caused the loss in quality, as if you look at the owls eyes, there is definition in the pupils.
Set your camera to continuous AF, use a single AF point for now - just the central one at the moment - and try and fill the frame in camera as you want the final image to look.
Oh, and the 200-400 should be used ahead of the 70-300 whenever possible, its a miles better lens - just look at Andy Rouse's photos if you need to see what that combo is capable of.
