This answer will compare and contrast the strategy and tactics from an American perspective in the European and Pacific theaters. One point of comparison between the two theaters is that both involved fighting an exhaustive and bloody series of battles with the eventual aim of either conquering or forcing the surrender of the homeland itself. Both the Germans and the Japanese had conquered a considerable amount of territory by the time the United States entered the war, and it was necessary for the United States to roll back these gains and bring the war to the core of these would-be empires. In both cases, this was done through heavy strategic bombing of German and Japanese cities, which was often carried out in such a way as to bring about , maximum destruction. In two particularly terrible instances, Dresden in Germany and Tokyo in Japan (among many others) were devastated by the use of incendiary bombs which caused firestorms.
These similarities aside, war in the Pacific and in Europe were very different in terms of tactics. First, the war in the Pacific was at first a war for naval supremacy, one in which aircraft carriers were essential. Once the Japanese Navy was weakened, the United States could begin the process of "island-hopping," taking one Pacific island after another from the Japanese Army, which had heavily fortified them. This bloody process, which culminated with horrific fighting on Iwo Jima and Okinawa in 1945, brought the American war machine to the brink of invasion by the late summer of that year. The destruction of Hiroshima and Nagasaki by atomic bombs, and subsequent Japanese surrender, made invasion unnecessary.