Was the Battle of Britain or the Nazi invasion of the USSR a more important turning point in World War 2?
Battle of Britain - The air war in 1940 and 41 gets all the press and Churchill's blessing as the 'finest hour' but even had Germany completely destroyed the British air forces, a very tall order, they'd have had a near impossible task in trying to occupy Britain. Thus you must look elsewhere for the turning point.
A more important turning point in the German-Anglo war would be the submarine conflict. This battle waged back and forth, mainly riding on technological improvements, for five years. Germany made some breakthroughs late in the war that might have turned the tide, but it was far too late in the war to affect the outcome. British improvements in long range aircraft and radar/sonar caused a collapse of German submarine initiative in 1943. Had Germany pursued their own technological initiatives earlier - very easy to do since they already had the information, just had not applied - they could very likely have continued sinking huge numbers of ships past the summer of 43. That could have prevented a major American build up in Britain (necessary for Africa/Italy 43 and Normandy 44) plus reduced the bombing campaign against German cities.
It is also arguable that the N African campaign might have been a turned point. Had Rommel defeated the British in Egypt summer 42, it would have greatly complicated the British war effort. Perhaps Iranian oil stops flowing to Britain (they ran their war effort in the African theatre with this supply), perhaps Turkey feels pressured to assist the Axis, perhaps India finally revolts against the tyranny of British occupation, perhaps British public opinion turns again Churchill earlier than in actuality and a peace candidate is elected in 1942 or 43....all possible outcomes to a Rommel victory that occupies Cairo and blocks Suez.
Russia: There is only one true turning point in the Russo-German war and that was Moscow 1941. Germany needed to take Moscow that year in order to divide the Russian front, to seize important transport/industrial centers, disrupt Russian government control of the country and generally demoralize the Russian people. Instead the main German effort was further south. While successful this theatre was not critical to the Russian war effort as the resources there could be replaced, with difficulty. Later battles at Stalingrad and Kursk were bloody and locally important but made little difference in the overall outcome. About all those battles could achieve had they gone the Germans way would have been to forstall defeat or at best, stabilize the front.
The Battle of Britain and Englands "finest hour" was a remarkable propoganda victory on the part of the English. However it is a much overplayed historical "turning point" and arguable in its significance. What cannot be argued is that 9 out of 10 Germans killed during WW2 were on the Russian Front. It was the Russians that decisively drained Hitlers Reich of both manpower and material. In effect, it was the Russians that beat the Germans with the allies in the west being more of a side-show. The Nazi invasion of the USSR could therefore be termed a decisive turning point in WW2 if one was to acknowledge the true impact of the Russians on the German War effort.