Not always but usually, I have a Pentax 12-24 which outperforms equivalent prime lenses regarding sharpness.
IQ isn't only just about sharpness though and primes often render images in a more pleasing way, offering better colour/contrast than a zoom. The sharpness issue between zooms and primes also becomes far less significant the smaller the aperture so if you mainly shoot landscapes like me the differences do become much more about rendering than sharpness - portability is also one of the advantages that primes have over zooms
Simon