I did some pixel-peeping comparisons between my cheapo 1.8/50 and 18-55 kit lenses. Surprisingly, the kit lens was very sharp starting wide open (f4@50mm). The prime, on the other hand, was very soft at f1.8, got a tad better at f2.8, and caught up to the kit lens @f4.
So, my personal conclusion... the kit lens is a better tool for me, since it is sharp wide open, has a good zoom range, and offers IS. Trying to sell my 1.8 on Craigslist.
Of course, your situation might be different. And if you do not pixel-peep as I do, the 1.8 aperture of the prime might sound really great. As they say, YMMV.
As for the original question... both have their places. Primes have an inherently simpler construction, so theoretically you get a better (sharper, wider aperture, etc) lens for the same money, or get same-as-zoom quality for less money. That's the theory at least.