Probably you are - but it's not so much of the camera, but the lens, and perhaps your skills. Particularly the flying ones require some skill as well as the right equipment.
Here's an example of what's possible:
This was taken with a 4mp camera, not your 16mp, and it's with a 500mm lens, rather than a 200mm. And I'd say that I was probably closer to the bird, too. So more than twice the lens and likely half the distance, making it considerably easier to get close in. I used a tripod; you had VR, but a tripod is better as long as the subject isn't moving too much - in this case, that is the case. The lens - an old manual focus one from the 1980s - is probably not as good as yours.
In addition, there are a number of other considerations. The Canon almost certainly produced a JPEG. What came out of your D5100? Was it a JPEG or a raw file? Assuming that it was a JPEG, the sharpness settings on DSLRs tend to be lower than on point-and-shoots or bridge cameras, since it is much more likely that a DSLR owner will want to post process the image.
Next, there's the consideration of just exactly what the AF was attempting to get into focus. In this case, you have a pretty tiny bird, surrounded by branches, nest and tree - all of which are at different focus distances. If you aren't careful about how you use the AF system, it would be VERY easy in this case to have the AF focused on something OTHER than the bird.
The flying birds are another story altogether. Were you tracking them, or did you simply try to get one in the middle of the air? Do you have AF-C set?
_____ Brian... a bicoastal Nikonian and Team Member
My gallery is online. Comments and critique welcomed any time!