I am 100% sure!!
Because if you are looking at DSLR lenses, a 100-400mm F2.8 willbex4 more expansive compare to a100-400mm F4.5 !!
With F2.8 you get sharper images because it lower the time of the exposure, If you use aperture priority and you set the aperture to f2.8 than you move it to F8.0, you will see the difference of the shutter speeds:-)
Boily