Yes, the Ritz is the Ritz and they have the Ritz Club which the London does not have - and which is, to me, a MUST on every Ritz stay. But at the London, you get a certain elegance and the big luxury of space - every room is a suite. There is, however, usually a very large difference in price between the two and the service level, while fine at the London, is not that same level of perfection you see at the Ritz. But really, I love em both!
For the same money? I'd contact the Ritz and ask what the daily supplement would be for Club access!