O'Leary, who has fronted The X Factor since 2007, said that he could not see either show becoming "exhausted".
"I don't think those shows are ever going to be exhausted," he told BBC Radio 1 Newsbeat. "They'll change in different ways and might be rested.
"That's a genre that has lasted in television for 40 years. It tells you something."
O'Leary added that he is not worried about The X Factor losing out to Strictly in the ratings or the NTAs, as the Simon Cowell show could benefit from its new "underdog" status.
"I think the public love an underdog and that's the thing," he argued. "Some years we win, some years Strictly wins. Personally I think that's really healthy for television."
Strictly Come Dancing beat X Factor, Britain's Got Talent, Dancing on Ice and The Voice UK to the 'Talent Show' award.
Speaking afterwards, Strictly presenter Tess Daly said that she couldn't imagine the show continuing without co-host Sir Bruce Forsyth.
[Strictly judge Darcey Bussell, contestant Kimberley Walsh and host Tess Daly with their National Television Award]
"I feel disrespectful even talking about him not being there because he's a legend, and I can't discuss him not being in the job while he still has it," she said.
Asked why she thought Strictly had managed to overtake The X Factor last year, Daly argued: "The standard of dancing was higher than ever before, from the off, really. And Darcey [Bussell] joined us - she's our lucky charm, I think!"
Photo gallery - National Television Awards 2013 winners: