Winston Churchill had military training and experience. I often forget that he had command experience in France during the Great War. Before that, he had been looking for opportunities to command in the field. He had many abilities besides being a naval administrator. When the situation had collapsed in May 1940, Winston was the obvious choice to lead the country.
Hitler lacked Churchill's experience and flare for the Supreme Commander role. That Germany did as well as they did was due to a number of factors. First was the dynamic and forward thinking army. There was some uneven quality, even in the German Army, but you saw giants like Field Marshall van Manstein, Has Guderian, and Rommel, to name a few. The second factor was their ability to produce technologically superior weapons. They often continued to use inferior hardware, but they could go from an army still equipped with Pzkw I's to the Panther in a short period. A feature of the early 1940's was that new weapons and technology could be developed quickly.
What Churchill particularly had was a high-level strategic vision. Hitler was more driven by politics and opportunism. You could argue that eventually, Germany would need to take out Russia, and June 1941 caught Russia in chaos. The German stroke came close to succeeding. Only the vast spaces and the work of some key generals saved them from defeat in the first few months. As it was, they lost large numbers of soldiers, mostly as prisoners of war, and immense quantities of equipment captured or destroyed.
Germany, though, under Hitler's leadership, was playing a gigantic Risk game. In 1942, they pushed as far as they could, until lack of resources and poor leadership at the highest level (Hitler's interference) dashed any hopes of success. Field Marshall von Manstein tried to rescue the situation, it was lost in the decision to tie up an army in Stalingrad. Improving Russian leadership, equipment, and manpower had grown strong enough to stop the German tide, and cause it to recede.