I like them both, but I'm definitely going to have to go with The Beatles. Also, no way can I come up with one favourite song... but I'll try to keep it under 10, haha.
-"I'm Looking Through You"
-"Tell Me What You See"
-"Things We Said Today"
-"In My Life"
-"You've Got to Hide Your Love Away"
-"I've Just Seen a Face"
-"Here, There and Everywhere"
-"If I Fell"
Shit, that's 11. Sorry. I'll stop there... for now. Haha.
The Beatles, by far. Every single one of their songs is awesome. Rolling Stones is more hit or miss, though I will say the radio doesn't do the band justice. Can You Hear Me Knocking?, Street Fightin Man, Gimmie Shelter, Central Park, Love Is Strong, Midnight Rambler, those are the songs that would be on my iPod.
I've gone back & forth between the 2 over the years. All comes down to my mood so for me it's a tie. I heard the Beatles first & they broke a lot of new ground artistically but I grew to like the edgier sound of the Stones later on. Then the old stuff of both grew on me again much later.
Beatles - Rain
Rolling Sones - Dead Flowers
The Beatles are arguably the most influencial act in the history of popular music, and I like their songs/albums better, so them. But both are great. John Lennon's Magnum Opus, Strawberry Fields Forever has got to be the best Beatles song.
I'm inclined to say "both" because I enjoy enough of the Beatles later work to basically equate that to my enjoyment of the entire canon of the Rolling Stones' work. It balances out nicely because I actually hate the majority of the Beatles' earlier work...
Now, to help, I considered that the Rolling Stones are still kickin' it pretty good, but whichever Beatles are still alive are taking it pretty easy...
I also considered that the Beatles seemed to have wormed their way into the American music scene with a well thought-out finesse, but the Stones just kinda...stumbled in, or something...
'I've Just Seen a Face'
'Norwegian Wood (This Bird Has Flown)'
'You've Got to Hide Your Love Away'
'And Your Bird Can Sing'
...or really any of the dozens of other Beatles songs that I would never dream of skipping when they come up on shuffle on iTunes.
Rolling Stones didn't really stand a chance. Yellow Submarine was one of my favorite movies growing up (and I'm still quite fond of it). Thanks, Dad!
Stones by far. Beatles are good, but I just like the Stones a lot more. Can't put down just one song, but my favorite album is Sticky Fingers. Might as well just be every song from that album as my favorite.