In a rare move, Apple chief executive Cook and his bitter rival, Alphabet boss Schmidt appeared at the opening day of a seminar organised in Amsterdam for the week-long Startup Europe Fest -- although they did not take the stage together.
And Schmidt, chief executive for Alphabet and former Google boss, triggered laughter when he revealed he had an iPhone -- made by his rival -- in his pocket as well as a Samsung.
"The Samsung is better, has a better battery. Are we clear?" he insisted. "And to those of you who are iPhone users, I'm right!"
At the top of the corporate world, Apple and Google are in a back-and-forth battle to be number one.
It's not clear which of the two Silicon Valley giants will emerge on top in a contest which highlights the contrast of very different business models.
The two companies have a virtual duopoly on the smartphone market, but Apple makes its own hardware and software while Google provides only the free Android software for handsets, including many made by low-cost manufacturers.
He also urged more European entrepreneurs to take a risk and get behind start-ups, saying Google was hiring thousands of Europeans every year because they had nowhere to go to on their home continent.
Apple was meanwhile on a mission "to bring the app economy to places where it's missed, because ... We recognise it hasn't gone everywhere yet and we want it to very much," Cook told the Amsterdam forum.
He also defended Apple from accusations that it was operating a kind of "closed" policy on its app store.
There were now two million apps on the Apple store, "that doesn't sound too closed. We do curate ... There's certain things we don't want to sell like pornography," he added.
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