We got Fed outside UNIQLO in NYC on Wednesday and asked him straight-up.

Obviously, Federer told us he's betting on himself ... but it begs the question, could Serena -- the greatest female tennis player of all time -- REALLY compete with Fed in a serious tennis showdown?

Remember ... Serena's been engulfed in this Battle of the Sexes subject for years. John McEnroe says he was once offered $1 MILLION by Donald Trump to do battle with her. Billie Jean King also threw herself into the conversation by saying there's no way in hell Serena would win a match with a man.

As for Serena's side on all of this ... her most recent comment on the issue came in the form of a tweet to McEnroe after he said "she'd be like 700 in the world" on the men's circuit.

"Dear John, I adore and respect you but please please keep me out of your statements that are not factually based," Serena said.

"I've never played anyone ranked 'there' nor do I have time. Respect me and my privacy as I'm trying to have a baby. Good day sir."

As for UNIQLO and why Fed was there rehashing the whole issue among so many wild fans -- the Swiss star just broke up with Nike to ink a $300 MILLION deal with the Japanese apparel giant -- and he was there to promote his new gear with the people.