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SANTA CLARA, Calif. -- The rivalry between Apple and Google is not for the faint of heart.

In fact, Google Executive Chairman Eric Schmidt said last week that the competition between the two companies is more "brutal" than ever, as the firms battle over mobile supremacy with their operating systems -- Google's Android and Apple's iOS.

Apple CEO Tim Cook and Schmidt have also taken jabs at each other's companies recently. Cook last month criticized companies like Google for their policies concerning users' data. On Thursday, Schmidt struck back, saying Google has "always been the leader in security and encryption." As for Cook? "Someone didn't brief him correctly on Google's policies," Schmidt told CNNMoney. "It's unfortunate for him."

But despite the fierce competition, when asked on Thursday night who his heroes are -- in the tech industry and outside it -- he had one answer: "For me, it's easy. Steve Jobs," he said in a quiet, contemplative voice.

"We could all aspire to be a small percentage of Steve," he said of Apple's late co-founder. Schmidt and former Google Senior Vice President of Products Jonathan Rosenberg were speaking to a full room of about 400 people at an event hosted by the Commonwealth Club of Silicon Valley here, promoting their new book, "How Google Works."

It's not surprising that Schmidt would feel that way about Jobs -- their old friendship has been well documented -- but the comment is nevertheless interesting given where the two companies have gone over the last several years. Apple and Google have been perennial legal opponents over patent disputes concerning their mobile operating systems. And the rivalry has taken another turn as both firms wade into smartwatches and the market for wearable devices.

Schmidt and Jobs met in 1993, when Schmidt was working at Sun Microsystems and Jobs was at NeXT, the computer company he founded after being ousted from Apple. Schmidt -- then Google's CEO -- was invited to join Apple's board in 2006, after conversations he and Jobs had over potential conflicts of interest, according to Schmidt and Rosenberg's book. But after mobile became such a large part of both companies' businesses -- Jobs famously vowed he'd go "thermonuclear war" over Android -- Schmidt stepped down from Apple's board, in August 2009.

In the book, Schmidt and Rosenberg describe Jobs as the quintessential "smart creative" -- an expression for someone with a combination of technical depth and creative talent.

"Exceptional people are worth hanging out with," Schmidt said on Thursday. "Because there is a good chance they are going to change the world."