The coaches will return for the second series of the show, along with Sir Tom Jones and Jessie J, on Saturday, March 30.
When asked if The Voice UK will be competing with the Simon Cowell series, O'Donoghue said to Yahoo: "No, it's a talent show, not a singing show.
"The only place you can put them up against each other is in the papers, we don't do that."
will.i.am said: "We're used to that, I can put my single out on a Tuesday and so can Danny.
"It's not like I'm threatened by his single, songs are songs, there is enough room for everyone to succeed."
The pair also talked about the fluctuating ratings for the first series of the show, which fell to as low as 4.49m during The Voice UK's semi-final show.
The Script frontman said: "It was our first season, we smashed all expectations, biggest BBC entertainment show in last ten years... incredible. But we have learned this year.
"The changes aren't drastic; they are just lengthening out the good bits of the show like the blind auditions. More people were watching us than the Brits."
will.i.am added: "Even the dip down, it was still a lot of people watching the show."
Photo gallery - The Voice UK series two launch:
Copyright: PA Images Ian West/PA Wire