News UK chief executive Mike Darcey has called the Guardian and Daily Mail digital "minnows" – despite the publishers' boasting a combined monthly online readership of almost 300 million – in the latest round of the debate about finding a sustainable model for professional journalism.

Darcey, who also criticised his rivals last month in a speech defending News UK's strategic decision to back the digital paywall model, offered a back-handed compliment about the Guardian's "digital first" strategy.

Darcey argued that the open digital strategy – coupled with cover price rises – will hasten the demise of print editions.

"Chasing online advertising revenue at scale requires a deep, free online proposition and this in turn undermines the incentive for people to pay for print editions," said Darcey, speaking at the Digital Media Strategies conference on Wednesday. "The Guardian web proposition is so good I wonder why anyone continues to buy the Guardian edition in print at all. They must be very wealthy people."

He added that aiming to rely on online advertising as the primary revenue stream was a dangerous strategy, putting newspaper publishers in direct competition with global giants such as Google and Facebook.

"When print is switched off, all you have is online advertising [and] online ad prices are low and are falling," he said. "If this is your only revenue source, then you need to think about the fact that you are head-to-head with the global internet titans. So while the Guardian boasts online metrics that seem impressive in our world and Mail Online seems huge with 190 million [monthly] uniques, they are both minnows in their revenue pond."

Andrew Miller, the chief executive of Guardian Media Group, the parent company of the Guardian, argued that ignoring the value of the internet giants is a fundamental failure to understand how readers use the web.

"Drudge [Report], Twitter, Facebook, Google, you have to embrace the models they are working with," he said. "These aren't our enemies, these are our friends."

He said that it was too simplistic and a mistake to automatically equate open access to content with a model that is free.

"Open is the way the web works. Open is about how you engage with your readers, about how people actually consume media today," he said, following Darcey with a presentation at DMS. "The days when you can hide behind something is long gone. Open isn't a luxury, it is not a nice thing we want to do, it is reality. Open is the way the web works, so we are working with the web".

Miller appeared to indicate that he might in the past have backed some form of paid-access strategy at the Guardian, but that the time had passed and the focus is now on the upcoming launch of the newspaper's paid members scheme.

"If we could do a paywall, of course we'd be doing it now because we'd love to do it," he said. "Unfortunately, that horse has bolted long ago, particularly in a world where in the UK, with the BBC, you have a big, free news provider … so that's reality. Membership to me is adding value over and above the consumption of news that people are willing to pay for."

Miller was promoted from chief financial officer to chief executive of GMG in July 2010.

Darcey also took aim at Mail Online's pursuit of the free ad model, but admitted that he would not like to see rivals fail.

"I want my business to succeed but I do have a broader interest in the success of [the newspaper] category," he said. "I would not regard it a great outcome if my titles were the only ones to be around. That doesn't feel like the world I want in the future. You need a plurality of voices. I do have a broader interest, even the Guardian [succeeding]. I want to win in the market but I do want the market to prosper as well."

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