For lens with the same focal length, shooting at the same aperture always yields the same results in terms of DOF and shutter speed. So whether the maximum aperture of the lens is f/2.8, f/4. or f/5.6, shooting at f/5.6 will yield the same results in those respects. Quality will most likely be best from the f/2.8 lens and worst with the f/5.6 lens, because most lenses are at their best stopped down a bit, and because if they're going to go to the trouble and expense of making an f/2.8 zoom lens, they usually try to use the best optics they can.
So the advantages of an f/2.8 are that the image quality is usually better, plus you have f/2.8 available if you need it. And if you do need it, you put up with the reduced DOF. "Horrid" is in the eyes of the beholder. Sometimes you *want* the reduced DOF, as it helps isolate the subject from the background.
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