I've had several people send me personal e-mails asking how I shoot raptors, particularly about what mode I shoot. Its a loaded question of course because depending on the lighting, lens, situation, what the bird is doing (and several other factors) makes a difference in how to take pictures. I'll just discuss raptors in flight for now. I always shoot manual mode so I control the aperture and shutter speed instead of letting the camera decide. This is what works for me and what I am comfortable with, but I have been photographing birds in flight since 1993, so I am comfortable how to shoot at under all conditions. To put it in perspective, I have over 20,000 Red-tailed Hawk pictures alone on my hard drive (after deleting the "throw-aways"). If you don't feel confident in doing so, DON'T. There are tons of photographers that take amazing photos, and everyone has their preference, so there is no single correct way.
Shooting in manual mode allows me to lock or unlock the aperture setting, but more important for me than that, is it allows me to change the shutter speed instantly with the turn of a dial. This is ideal for shooting moving subjects in many situations. If you choose to let the camera decide the shutter speed for birds overhead, the camera will underexpose and overexpose a number of photos. Yes, you can use exposure compensation, but that might still leads to 'misses' in exposure. Check out these photos of the same Cooper's Hawk taken seconds apart. The "sunny 16" rule normally does well (for topsides or birds at eye-level) when the sun is directly exposing a bird, but when the bird flares overhead, I like to choose the exposure. I shot the underside of this bird at f4 -- 1/800 sec. (200 ISO), and the topside at f4 -- 1/2500 sec. (200 ISO), changing the shutter speed as the bird turned. Again, this takes lots of practice, so it may not be for everybody, buts its the way I feel comfortable.