Elsa, I must agree with Tommie, the original image is definately a stunner.
With regard to the glossy, I must confess a great fondness for these birds. They can make stunning images, and had you used the D800 this particular one would have been the most stunning one I have yet seen. It just lacks that little bit of extra dynamic range to lift the shadows on the back a bit...
I know we have discussed this before, but Albert Froneman who is probably one of SA's best specialist bird photographers says that full-frame is much better for birds, and I think this is why he feels that way.
The only possible exception is the D500, but only because no one I know can afford a D5...