O'Leary, who has fronted The X Factor since 2007, said that he could not see either show becoming "exhausted".
© Ken McKay/Thames/Rex Features
"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.
© BBC
"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.
© PA Images / Dominic Lipinski/PA Wire
[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:
Copyright: PA Images Dominic Lipinski/PA Wire
