Home is where it's born, so England. It thrived in the states for a century but the Europeans have been coming on strong.
The sport as we know came out of England, we all know that... But technically speaking, fist fighting as a sport was around in the ancient Greek times. It really depends how you look at it I suppose. For me, the true spirit of boxing over the last century has been in the USA. The popularity of the sport flourished over there and the sport most likely wouldn't be as rich in tradition, folklore, memories etc if the States hadn't taken it to their hearts.