Eric Schmidt knows what it is like to cross swords with the most fearsome competitor in the technology business.

The chief executive of Google has come up against Microsoft twice in the past, each time with mixed results. That may help to explain why, even as Google's fortunes blossom, the veteran technologist is eager to avoid a question that arouses obsessive interest in tech circles: whether a showdown with Microsoft is looming that will determine who becomes top dog in the online world.