Unfortunately, this argument is not entirely correct. If we drop the stones from a sufficiently tall building or cliff, they will reach terminal velocity (due to air resistance) and then the larger stone will indeed go faster (if they have the same shape). However, if we tie them together then the resulting speed will depend on both the increased mass (which, all else equal, will increase the speed) and the new shape (which could potentially increase the drag force).
However, Galileo's argument is sufficient to show that a model that only considers mass, to the exclusion of all other variables, is indeed defective. It just isn't sufficient to show the universality of free fall.
I first came across this argument a very, very long time ago, back when dinosaurs roamed the earth and Pets.com was a good buy and I was in grad school. I read Jacob Israelachvili's book on intermolecular forces, and he included Galileo's argument in the first chapter, along with an assertion that the argument is wrong, but he left it as an exercise for the reader to figure out why the argument was wrong. It took me a while to figure out the problem with the argument.