Heavier car will also have more traction to use towards cornering by the same factor x. So both cars will be able to corner at exactly the same speed, at least in the idealized case.
Realistically, less tire deformation might give a lighter car a slight advantage.
Another real world consideration is that when you load the car, increasing its weight, you usually raise the center of mass as well, increasing risk of the car tipping over in a turn. But this is all about the height of CoM in relation to wheel base, and isn't directly tied to car's weight.