I think a big industrial society would have developed anyway in North America, but it would have done so more gradually under British rule...as there would not have been nearly such a driving, competitive motivation to compete with Britain as arose with the emergence of the 13 colonies achieving independence.

How all that would have affected the various European wars is pretty hard to say.

England would, in any case, have benefited tremendously from having all the resources of North America at its disposal, so the British Empire would have been in an even stronger position historically vis a vis other European powers than it was during the 1800's and right through to the present era. England was really the world's one superpower for a time there...from the defeat of Napoleon until the onset of the First World War. WWI critically strained British financial resources and their empire began to subtly weaken from that point on...although that was not really apparent to people in an external sense until the post-WWII era unfolded after 1945...at which point the USA began to emerge as the next one world superpower. The Soviets tried to compete on an even basis with the USA, but actually they couldn't. It took about another 40 years for that to become clear.

China will probably emerge as the next one world superpower. We'll see...if we all live long enough.

One thing for sure. Nobody stays on top forever. But they all think it will be forever while they are there. ;-)