The New York Times quotes Harvard Business School (HBS) professor David Yoffie as saying "the right way to think about" Google Inc. (NASDAQ: GOOG) is as "the next Microsoft Corp. (NASDAQ: MSFT)." Setting aside for the moment, the arrogance that we need Yoffie to tell us how to think is the simple notion that he's wrong.

Here are three reasons why:

• Google is an innovator, Microsoft never has been. Microsoft got started by licensing an operating system for the PC. And it prospered by making it the dominant operating system and tying it to office software -- each component of which it copied or bought from an innovator. Google has won because it has developed an improved a search ad technology that gives advertisers a higher return on their investment;
• Google has succeeded because its product works better, Microsoft's not so much. Microsoft has lost market share in search advertising since it started to focus on it -- watching its share fall from 11% in 2005 to 5% today. The reason Microsoft has lost share is that its product simply does not work as well as Google's; and

• Microsoft can't compete with Google's superior algorithm in search advertising so it's trying to acquire its way in. Microsoft in the past has tried to take markets away from innovators by copying their products and using its operating system power to force people to use them. But this strategy is not working for Microsoft so it tried, unsuccessfully to do something it's never done well -- buy market share through acquisition. Google bought YouTube -- but not to take share from an innovative incumbent. Instead, Google wanted to use YouTube as the basis of creating a new market -- video search advertising.

This may be just an academic debate, but I think it matters for investors. If you think of Google as Microsoft, then you should sell it now. That's because Microsoft stock is down 44% from its January 2000 high a few months before Steve Ballmer took over as CEO while Google's has gone up 631% since it August 2004 IPO.

Despite its vast capital resources, Microsoft simply cannot innovate and Google can. That's why it matters that an HBS professor is telling you the wrong way to think about the two companies.

Peter Cohan is President of Peter S. Cohan & Associates. He also teaches management at Babson College and edits The Cohan Letter. He has no financial interest in the securities mentioned.