What were some similarities between the European and Pacific theaters during World War II?

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...

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.