Nothing. If you turn both volumes up the tones will do the same thing. However, on the LP, the way you would use it is by switching between the front and back and at that point the position of the tone control would matter on that pickup.
Not only that, on an LP the volumes also can kill each other - turn the volume of one pickup to zero, and then put the switch to both pickups, you won't get any sound.
But the easy way to show, if you have an LP, try it. Turn one tone full down and one up, switch betwen them, you will see one is muffled, one isn't, switch to both and it will be muffled.