It's funny - Sympathy for the devil and Strawberry Fields are also my favorites.
I love them both, but if I would have to choose which music to take to an island, it would be The Beatles.
It's been mentioned many times before that The Stones were the better live band. I was lucky having seen them twice.
But even more important: The Stones have many more songs you can dance to. The Beatles just a few. Most of their rock'n'roll stuff is on their early records. Their last dancing number, I would say, is "Drive My Car" on Rubber Soul.