As a band the Beatles were far from overrated, but the songwriting duo Lennon/McCartney was somewhat overrated. When they worked together, they churned out a ton of formulaic pop songs. Its was a big deal at the time because they dominated the charts and few acts wrote their own music. But "Love Me Do" isn't exactly the pinnacle of lyric achievement. And when the Beatles began churning out songs that broke the Bealtemania formula, John and Paul had quit writing together, with scattered exceptions.
Jagger/Richards might have been the same. I don't know as much about the Stones as i do the Beatles, due to the amount of books out there about the bands. From what I understand, Mick and Keith wrote together a lot until after Tattoo You.
Your future's all used up.

I prefer Jagger/Richards and the Stones, myself.
What do you think this is, a signature? It's a way of life!

Christ, this again.
Lennon & McCartney, obviously. You need far more musicianship to write their songs than the Stones'far, far more.

Jagger / Richards
The Stones are in my top ten artists of all time. I'm not sure if The Beatles would even make the top 100. I don't hate them or anything I just don't think they're at all special and they wear very quickly.
http://www.haneke.net/

No worries.
b l u e
g r e e n

Not that I am mildly interested in debating minutea or even history.but I never said The Beatles did all those things first over anyone.but they were certainly in England the front runners and certainly ahead of the Stones in bringing a hell of a lot to the wider public table early.
And unlike a lot of folk here.I was around thenI am that old.
But if it is important to someone that Joe Blow played sitar on a record before The Beatles or Nobby Clark cracked America first etc then hey ho and all power to them.
GOOD SKY YOU'VE GOT HERE McCINTYRE..WELL DONE!!!

Funny, but also untrue
b l u e
g r e e n

Whoops..my mistakethe Stones did them all before the Beatles.
GOOD SKY YOU'VE GOT HERE McCINTYRE..WELL DONE!!!

None of those things were done first by The Beatles.
b l u e
g r e e n

If pressed, I would say that the experimenting with wider musical layers.as on Revolver and Sgt Pepper predating Satanic Majesties.
The shift away from being a covers band to writing their own material..remember that the first Stones hit was written by John and Paul.
The 'cracking' of America.
The promo/video concept with new single releases.
As a bandthese are the reasons the Fabs beat The Stones for me.as for the Original question , John & Paul or The Glimmer Twins.they have both produced many, many songs I adore and revere so I have to repeat that I love both flavours of ice cream and would not be mithered to choose one pair over the otherand thank the powers for both of them being around.
GOOD SKY YOU'VE GOT HERE McCINTYRE..WELL DONE!!!

WOuld you mind giving a couple of examples of what you mean by "popularised a lot of stuff first"?
b l u e
g r e e n

I adore them both.
Gonna lean slightly towards John & Paul and only because they did and popularised a lot of stuff first and were funnier guys.but I cannot imagine and I shudder to think of a world, a youth, an adolescence and even a present without either The Beatles or the Stones.
Horrid.
GOOD SKY YOU'VE GOT HERE McCINTYRE..WELL DONE!!!

Lennon/McCartney. And IMO, Lennon was a very underrated guitarist

I would have to go with Jagger/Richard since Lennon/McCartney didn't write that many songs as a team.
They began writing as a team but by 1965, were a team in name only. George Martin said their relationship as songwriters was very much a healthy competition.
God knew he was good and God did look the other way that day.

Lennon / McCartney
But you have to hand it to Jagger / Richards for longevity alonebest married couple ever.

Well there's that old tale about the first time The Stones met Allen Klein and he asked who made the band's records and everyone pointed to Keith.
Normal Is A Myth.

Although it's not that cut and dry regarding who did what with the Stones' songwriting, I'd agree that Jagger / Richards worked better as a musical partnership.
Eh I don't know what 'phallocentric' means, but NO GIRLS!

Jagger/Richards. I know I'm biased, but I like the Stones, but I never cared for The Beatles.
Roger Waters and David Gilmour are Bronies

Lennon/McCartney

Lennon/McCartney
"Worthington, we're being attacked by giant bats!"

Jagger/Richards
What are words for when no one listens anymore

Stones, 'cause of their spirit. I can picture Richards swinging with his guitar and Jagger dancing and singing, beyond the grave.

Lennon/McCartney. They were just better.

Cheers!

Stones Stones Stones Stones Stones
. . . But I do like the Beatles, too.