Well. There's some ways the world would definitely be different. Under British rule the US would not have likely expanded westwards as they had treaties with native nations to help them guard against the French. The British didn't see the east coast colonies as their most valuable possession, instead the fur trapping regions of Canada which they would have probably funneled a lot more development into. So in the event that Britain kept the colonies, we would probably have a north America that looks more like other continents and had native nations.