There are many differences between the European and Pacific theaters during World War II, including that the US entered the Pacific theater in response to the surprise attack at Pearl Harbor. According to the National World War II Museum,
On December 7, 1941, Japan staged a surprise attack on Pearl Harbor, severely damaging the US Pacific Fleet. When Germany and Italy declared war on the United States days later, America found itself in a global war. Japan launched a relentless assault that swept through the US territories of Guam, Wake Island, and the Philippines, as well as British-controlled Hong Kong, Malaya, and Burma. Yet, with much of the US fleet destroyed and a nation unprepared for war, America and its allies decided they needed to save Great Britain and defeat Germany first.
Conversely, the US deliberated for a long period of time over whether to join the Allies and enter the war in Europe. Before Germany and Italy declared war on the nation, President Roosevelt had many meetings with Winston Churchill, who was imploring him to bring US force to the European theater to help shorten the war.
Nevertheless, there are similarities between the two theaters. The war in both territories was difficult and deadly for the US. Unlike Germany, which had a large group of trained soldiers, the Japanese army had a small corps of officers who were professional military men. Most of the soldiers were relatively inexperienced. Even so, while the Japanese military might not have been as skilled or well-equipped as the German army, the Japanese fought aggressively.
Racial conflicts underpinned both fights. The war in Europe was launched by the German notion that German Aryans were superior to other peoples. The war in the Pacific was launched by the Japanese and also had racial overtones on both sides, although they might have been more nuanced.
Both theaters involved several countries. In the Pacific theater, the war was led by the Japanese against US and British territories. Moreover, the Japanese were fighting in partnership with the other Axis powers, Germany and Italy. In the European theater, the German-led fight encompassed military launches against Poland, France, Russia and many others. Similarly, the Germans were in agreement with the other Axis powers, Italy and Japan.
The war in both territories concluded when the Axis fighters were overpowered by the Allied forces. The war in the Pacific ended with the detonation of the atomic bomb, while the Nazis eventually were overcome by the approaching Russian and US military forces.
The main similarity between the European and Pacific theaters of operation during World War Two was the nature of the adversary against which the United States and its allies were fighting. Both Imperial Japan and Nazi Germany were governed by militaristic autocratic regimes. Japan, under Emperor Hirohito and, more significantly, Hideki Tojo, was entirely militarized with the goal of expanding its territory and access to natural resources, leading to the invasion of Manchuria in 1931 and subsequent invasions of Southeast Asia and the Philippine Islands. (Japan had already, in 1919, colonized the Korean Peninsula.) Germany was governed by the National Socialist German Workers Party, or the Nazis, under the leadership of Adolf Hitler. Hitler, like Tojo, was determined to expand his country's borders both to incorporate more territory with which to feed its large and growing population and to secure access to natural resources, specifically the oil fields of the Caucasus and Romania. Whereas Japan had invaded China and Southeast Asia both to secure land for growth and to access resources, including oil and rubber, Germany invaded Russia and the Ukraine for the same reasons.
Both the European and Pacific theaters represented expansive regions requiring enormous numbers of troops and ships, and both involved military operations designed to move Allied troops closer and closer to enemy homelands. The European theater actually started in North Africa, as U.S. and British forces found it necessary to defeat German forces there in order to gain a foothold with which to eventually attack Continental Europe (through Sicily and mainland Italy). In the meantime, Allied forces were gradually built up in England for the purpose of ultimately invading Europe from the north--the D-Day landings of June 1944.
The comparison with the Pacific theater involved the "island hopping" campaign orchestrated by U.S. General Douglas MacArthur. Because of the range limitations of American bombers, island chains across the Pacific had to be secured so that the U.S. could construct airfields on the islands that could then accommodate those bombers and extend their range closer and closer to mainland Japan. The battles for these island, such as Guadalcanal, Iwo Jima, and Corregidor, were among the most intense of the entire war, and U.S. Marine Corps and Army fatalities were enormous. The toll in Japanese lives was even greater, due in no small part to the fanaticism that had been instilled in Japanese troops defending the islands.
Another similarity between the European and Pacific theaters involved the efforts of the United States and Great Britain to resupply its forces over long ocean routes. German submarines in the Atlantic and Japanese submarines in the Pacific both exacted a costly toll on Allied shipping.
In the European and the Pacific theaters, the United States faced a well-trained, well-disciplined, and initially well-equipped enemy. Both the Japanese and to a somewhat lesser extent the Germans (many of whom, by the end of the war, were conscripts) were fanatically devoted to their cause and reluctant to surrender. This was especially true of the Japanese, who had a strong cultural bias against surrender, which made them both difficult to defeat and especially brutal toward American captives. Strategic air power was important in both theaters, as the Allies reduced almost every major city in Japan and Germany to rubble before finally forcing surrender. Indeed, the Japanese were forced to surrender by the devastating might of American air power without the necessity of a ground invasion. Obviously the Pacific war was more of a naval war, but both theaters witnessed massive amphibious assaults on such beachheads as Anzio, Normandy, Saipan, and Iwo Jima. Some of the city-to-city fighting that characterized the conquest of France and Belgium was also witnessed in the Philippines. Obviously, there were many differences between these two conflicts—World War II for the United States was in reality two different wars—but in terms of human loss and the amount of military power that had to be brought to bear in order to achieve victory, they had much in common.