PlayStation 4 sales crossed the 6 million milestone earlier this month, whereas Microsoft hasn't updated its Xbox One sales tally from the 3.9 million mark it revealed in January.
"We have a fantastic lineup we’ll reveal more of at E3 and beyond," added Harrison. "We have a lot of great surprises to come."
Titanfall is, as you might expect, also seen as a key plus point for the Xbox One. "Titanfall is blowing the doors off, literally and figuratively. Great engagement, just fantastic proof of users not only buying Xbox One, but using it in a very engaged way. More than five hours average use per day, which is amazing."
Harrison was talking at GDC 2014 to promote the company's ID@Xbox scheme, which is designed to tempt indie developers to create software for Microsoft's latest home console. He also referenced the fact that the Xbox One will launch in an additional 26 countries in September.
"That will be 39 markets where Xbox One will be available by the end of the year," he said. "Partnering that with the ID@Xbox program means that I hope we find really culturally relevant local products and experiences coming to our platform. That will really accelerate us."