As I move up to heavier kettle-bells for my swing, I've been sticking to using two kettle bells instead of one. So I'll do a 2 hand swing with 25lbs on either hand instead of a 50lbs swing. Does it make a difference ?
It would change the movement completely. like using dumbbell vs barbell.
One handed would bring in more little stabilizing muscles and it would allow more development of your weaker side. While 2H would be better to develop base strength as you have more control.