I dont know much about cars and related stuffs, but big tyres really better in cornering than small tyres? or, maybe there is some explanations.. sorry, im not car expert hehe
Is because when you go for bigger rims, say 14" to 15", you need to lower the aspect ratio (tyre sidewall) so that the overall diameter stays as close to your original size.
In 14" I am sure you are either using 175/65R14 or 185/60R14, so when going to 15" you need 195/50R15 or 195/55R15.
Why in 15" it handles better?
1. Tyres are wider, from 175 or 185 to 195mm.
2. Sidewall lower, less flex, means less body roll.
3. you have choice of performance tyres, so traction better.