Over the past three decades, a few titanic rivalries have defined the technology industry’s megatrends, ultimately determining which products eventually end up in consumers’ and companies’ hands.

Now, adding to the annals of competition that include Microsoft’s (MSFT) clashes with Apple (AAPL) in the ’80s, IBM (IBM) in the ’90s, and Google (GOOG) in this decade, the new defining rivalry in tech may be between Google and Apple. Google CEO Eric Schmidt‘s resignation from Apple’s board on Aug. 3 highlights the degree to which these companies are more foe than friend.

By most measures—revenue growth, stock appreciation, magazine cover stories—Apple and Google are the two most successful and influential companies of the past decade. Yet their visions for how the computer industry will shape up in the next one could hardly diverge more. “They are both very innovative companies with very different ways of innovating,” says Henry Chesbrough, director of the Center for Open Innovation at the University of California at Berkeley. “They’ve both been very successful, but there’s a contest of different approaches going on here.”

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