It's not the size of the wheels, it's the size of the tire sidewalls. Old Mini Coopers had (and still have) incredible handling, and they had 10" wheels.
If you take one car, NOT three different ones, and you try different wheel/tire size combos on it, you will get better handling with the larger wheels. Why? Because in order to keep the speedometer accurate, when you increase the size of the wheels, you have to decrease the height of the tire sidewall. When you do that, the shorter sidewall will flex less, which means you get better handling.
comparing 3 different cars and saying the car with the smaller wheels handles better and therefore wheel size doesn't matter simply doesn't make sense. Sure, my CRX with the 13" rims will handle better than a semi with 21" wheels, but that's not really a function of the wheel size, is it?
But my "good" CRX with 15" wheels handles much better than the winter one with 13" wheels, and they both have the exact same suspension.