Good focus on the eyes and sufficient DOF to get all the information on the Owl but subdue the background.
The wind blowing the feathers made me smile, the Owl looked quite offended
I've put up a mod which you may think adds some more detail
I've just spotted that this is only your third bird pic, I'de say you are doing well.
On the question of aperture, I think f4 was a good choice, as I said, you've got quite a good blur of the background. In part you may have been limited by the distance between the bird and the background - if its too close its difficult to get an ideal out of focus effect.
You are using the right lens for this type of shot, have you tried it at f2.8? It may lose you some of the feather detail but if you focus spot on the eyes you may find its even closer to what you want.