The number of Netflix subscribers in the United States has overtaken that for HBO, at least according to some headlines. Netflix is aiming to double or triple that. However, Jeff Bewkes, the chief executive of Time Warner, which owns HBO, argues that television is taking over the internet rather than the other way around.

Netflix added another two million members in the United States in the last quarter, taking the total of paid up streaming subscribers to 27.9 million. The total number of streaming members, including those not currently paying or on free trials, rose to 29.2 million.

At the end of 2012, HBO had 28.7 million subscribers, according to data from SNL Kagan. So Netflix is not quite there yet, although it is forecasting to reach 28.8 million paid subscribers in the United States within three months.

Netflix now has 6.3 million paid subscribers outside the United States, or 34.3 million worldwide. HBO has 114 million subscribers globally, through bundling with other pay-television services.

Nevertheless, Netflix can claim an increase of nearly 3.9 million paying subscribers worldwide in the last quarter, or 9.8 million over the year.

In terms of the total available market in the United States, Reed Hastings, the chief executive of Netflix, told analysts he believes there is room to grow two to three times the number of subscribers.

“Our best guess is that the market for a service like Netflix because it’s less expensive than HBO, it’s got more content, it’s all on-demand, it’s personalized, it’s on multiple devices, is somewhere in the two to three times HBO, or 60 million to 90 million. And we’ll only know that with any confidence when we get there.”

The chief executive of Netflix has previously said: “The goal is to become HBO faster than HBO can become us.”

The company has indicated that it will concentrate more on exclusive and selected programming, rather than non-exclusive bulk deals. It will also continue to invest in original programming, although this currently represents a relatively modest proportion of its total programming budget.

“Our appetite for non-exclusive content is going to near-zero,” Ted Sarandos, the chief content officer of Netflix, told delegates at the FT Digital Media Conference. “We are willing to pay more on an exclusive basis.” He said consumers get confused if non-exclusive bulk programming is available on several online services.

Speaking earlier at the same conference, Jeff Bewkes, the chairman and chief executive of Time Warner, repeated his claim that “TV was taking over the internet, not the other way around”.

He said that the amount of time that people are spending and their engagement with video is increasing and this is made more valuable through on-demand viewing.

He agreed that online video from providers like Netflix would become increasingly important in the future but suggested that it would be increasingly difficult for them to continue to grow their subscriber levels in their home market.

“Every time you add subs, your disconnections grow,” he said. “Once you get into the 20 millions, it is very hard to go as fast as before, but he conceded: “Maybe it will get to 40 million.”

“Netflix is a pretty good company,” he said. “It is not at all surprising that they have the subscriber count they have.”

While globally HBO has significantly more subscribers than Netflix at the moment, the rate at which Netflix is growing is impressive, assuming it can maintain the current momentum.

The difference is that pay-television subscribers may not necessarily have a choice whether they pay for HBO, whereas Netflix is a standalone proposition.