Hmmm. What if United and Chelsea wanted the same player? United are a bigger club, but I reckon 50% of players would take Chelsea simply because they wanted to live in London. Alexis Sanchez was massively swayed towards Arsenal over Liverpool because London has specialist Chilean schools for his kid/s. London is it's own city state in so many respects, it just doesn't compare with our great Northern cities, and Spurs have been the beneficiaries of this to some extent.
United are a club that exist in it's own universe, and they attract the best players simply because of who they are. Even though the city of Manchester has had a huge say in the clubs culture and the make up and attitude of its fan base it wouldn't matter in this day and age if they were based in Manchester, Carlisle, Exeter or York, they are a club that players want to play for. City on the other hand just pay massive wages, and this is a big equaliser when you're competing with London clubs. So, I don't think it's a great example.