The big difference is the F-stop number. The lower the number, the more light it lets into the sensor. That means sharper images. You will see that at a lot of sporting events and air shows, very big lenses. They are typically 500-600mm focal lengths at f2.8. The one I have is F4.0. For most applications, it's fine if you know how to take advantage of it. F2.8 is very forgiving and does make for some incredible pictures.
In this case though 200-500mm zoom at F2.8 is a bit overkill. Most f2.8 lenses are either a smaller zoom range, or they are prime lenses, meaning no zoom, a fixed focal length. Prime lenses also have much sharper images because of the fact they don't have to tune lens glass to sweep through a range of focal lengths. They are dialed in perfect for the size.