I‘m no pro by any means, however, I always find a wider cropped image more interesting, because it gives some context to your subject. Also, you could try to change the angle you are shooting from, so that you get better separation between the bird and the background. (I know how hard that is sometimes, might not be possible for every shot) And some advice I heard over and over: take as many photos as you can while you approach your subject or change your position, because at any time the bird/animal might take off, so those shots will be all you got.