dino21 Loc: McAllen, TX

Lighting...... Full moon is frontal lighting, anything else is side lighting of varying degrees.

Appy Loc: Flint Hills (Ks)

I was very surprised to see that my favorite of the two shots is the top one using the faster shutter speed. My logic would suspect some sort of vibration occurred to fuzz the second attempt. But it may be something else. One thing I've heard time and time again is that lens tend to lose sharpness when maxed out to full length. So instead of shooting at the full 600mm you might try backing off to 580 or 550. I doubt there will be much noticeable difference in terms of frame image, but if there is a sharper image at somewhat less length it could easily be cropped to equal frame size less sharp 600mm shots are producing.
I am not a pro, so take what I say with a grain of salt. Just trying to help with ideas to consider.