It's pretty hard to tell. I've read a lot that Paul was, because he's cute and charming and likes to put on a show. Like in the authorized biography, Ringo says that if fans of each Beatle lined up behind him, Paul would have the longest line. And at the end of the Anthology book, John says that Paul was the epitomy of what the Beatles were, and says that he was always more popular with the kids and the girls. It's sometimes hard to judge it on the opinions of teenage girls, because they just love him for his looks. But, Paul does have a lot of fans, still even today, that love him. Male, female, old and young.
It also seems like if you asked a non-fan to name a member of the Beatles, they would probably answer John Lennon, but maybe some would say Paul too. I asked a friend of mine if she knew any, and she said "I know that Paul dude". Before I was a fan, I probably would've said John if I was asked.
But George, as I'm discovering, does have his share. I found on a website somewhere a bunch of letters written to the Beatles in the '60s, and a lot were written to George. And Ringo, of course, got the most fan mail at one point. Also, on the Ed Sullivan shows, when each Beatle's name was mentioned, they all got about an equal amount of screams.
But, you can't base it on screams and who teenage girls think is the cutest. I think that John and Paul probably are the most popular, they wrote most of the songs and are just the most well-known and had the most successful solo careers. They probably tie, I think.