I would have to say that as a general rule rule, yes, primes are sharper than zoom lenses. The most obvious reason being simpler construction (fewer groups/elements) and working at only one focal length. There is also the principle that
lens is going to be sharper when stopped down. You have to stop down a f/1.8 lens 1 1/3 stops to get to f/2.8. By simply physics alone, the prime will be sharper. And lets face it, not many people are running out and dropping almost $2000 on a Nikon 24-70 f/2.8 lens, which is a truly great lens and sharp wide open @ f/2.8. I have yet to have any type of consumer zoom or even third party f/2.8 lens be as sharp at their widest apertures as a prime lens will be
at that same aperture
. Again, one reason being that the prime is stopped down at that point. And some lenses, such as "superzooms" will never hold a candle to a prime lens. That said, I shoot with a 18-200mm lens all the time. It is a matter of understanding that
lens is a compromise to achieve a result. From engineering to use in the field. I use the "superzoom" so that I don't have to swap lenses all the time. The consequence is that image quality suffers.