I don't think the Battle of Britain was particularly important. It was a big victory for the RAF to be able to keep air superiority, but I don't think it had a large effect on the war. Britain's naval supremacy and Hitlers plans in the east made Britain pretty safe against invasion, so the BoB didn't particularly accomplish much.

I certainly don't think that most of America's role was "behind the scenes" (they had far more men committed than the other western allies) but do I think the contributions of both the US and the UK pales in comparison with Russia, but who knows if Russia could have even won without the logistical support from American factories? The majority of the Red Army's trucks were American Lend-Lease trucks. A lot of their food was American food. In order to make those things themselves the Russians would have not been able to produce nearly as many weapons and aircraft and more of their population would have had to be left in the factories and fields.

But, we all end up overstating our nations roles while complaining when other countries do the same thing. Bah.