In results of a clever blind test of search engine queries, Google is running slightly ahead of Bing and Yahoo, but not by much.
This shouldn't be too surprising. The algorithm itself can be approximated. Idealab experiments for the search engine Snap proved this many years ago. On a blind basis, it's difficult to tell the differences. Google's conumser-facing advantages aren't so much the algorithm as the brand. Google has come to mean search. Google has become a verb. Google also brilliantly protects its brands by offering a huge set of other consumer tools and services for free.
Equally important as Google's brand are its enormous economies of scale and scope. These advantages include:
-- A much, much larger penetration of advertisers and their budgets
-- Lower operating costs per dollar of revenue
-- A technology platform that allows very rapid introduction of new services
And all of these advantages are self-reinforcing.
I'd expect Bing to take some market share from Google and Yahoo and perhaps cause Yahoo to update its negotiating stance with Microsoft. But I wouldn't expect things to change too much very fast.