I like the flight image and the BG. I'm looking at this on a poor monitor at work, but feel that your focus might have just missed the eye (but, with this monitor, I might be wrong).
The tonalities look good for natural light. You might try positioning a reflector to light the bird's underside, if you haven't. The belly looks good but it's very dark under the chin. But that may just be because of very dark feathers there.
Very hard to tell at this size, but it doesn't look really sharp to me. You are the judge of that, by looking at the raw file at 100%. If it isn't sharp there isn't much you can do. If it's just slightly off, some sharpness can be eked out. It takes 3 or more flash units to get them really sharp (2+ on the bird, one on an artificial BG).
These guys are fun to shoot -- keep at it! Good AF is key.