That's not quite right, the history of both sports starts with English Public (private) schools, most would have their own rules for a game involving one ball, two sides and 10-20 players on either team.
The game most resembling football was played at Charterhouse and it was from here that the official FA rules were formed.
Rugby, Warwickshire, was where the game most similar to Rugby was created.
I've played both at quite a high level, maybe football slightly higher and I don't think you can say which one is better.
I would say that football is more widely played for a reason however. It's simple to play, not expensive and doesn't have very complicated rules.