Not to be a Gilligan, but both sides have excellent points. They are both just awesome bands. I love the Beatles and Stones pretty much equally. I still am in awe of the incredible output of great songs from both bands. I played my Rubber Soul record the other day and my 4 year old daughter, said "Daddy, I love this music." She likes the Stones too. Tattoo You is a big hit. She dances like crazy to it with her best friend.
I think The Kinks deserve an honerable mention too. Their catalogue is pretty outstanding.