Band of Brothers did take place in the European theater but more specifically the combat took place on the western front and the characters were American. The American experience of the "European theater" is different than say the Polish/Soviet or even occupied countries like France/Netherlands.

One example that comes to mind is the treatment of POW's. Nazi's generally treated Western POW's comparatively well and the rates of POW death for example are very low when compared to POW death rates of Japan. The rates of death for non-western POW's under the Nazi's is very high. So by POW deaths there is "brutality" in both theaters but the Western front is less brutal than the Pacific. There were also factors like Japanese cultural attitudes towards surrender which led to very high casualty rates among the Japanese and a lack of trust in surrender. There are cases of fake surrenders by Japanese soldiers being used to kill Americans, and Americans executing surrendering Japanese soldiers.

So it depends on your question, asking about the contrast in the experience of an American soldier between "BoB" vs "The Pacific" is different than asking which theater is more brutal, Eastern theater vs Western theater. From what I've read the Pacific is more brutal in the first sense but not necessarily in the second.

One simple answer to this is racism. While there was extreme anti-German sentiment into the First World War, and definitely continued in some degree to the second, America was highly populated by German-speakers, and people with German ancestry. Compared to the Japanese, Germans had an "understandable" culture. Not to mention the many in America who sympathized with, or even supported the Nazi party initially.

With the Japanese, however, the animosity goes back much further. (See: Yellow Peril and the Gentleman's Agreement). Anti Japanese sentiment was prolific in the US for 40 years and more prior to Pearl Harbor, especially on the West Coast. Added to that, is that as the war began, we had been personally targeted by Japan. Americans saw other Americans being killed and wounded at Pearl Harbor, knew of them being marched to prison camps in the Philippines, and knew of the valiant stand at Wake Island. Putting all of that together by 1942 meant many Americans have something of a grudge against Japan more so than Germany (See Max Hastings, Retribution for a good take on this leading to the use of the A-bombs).

Added to this, is a fundamental difference in the way the way is tactically conducted on the ground. I've read very few accounts of Germans committing mutilations on American prisoners. u/Soft-Rains is correct in this, that BoB only shows you one front of the war. Going back to the Pacific, American (as well as British) soldiers and Marines found themselves combating an enemy that did things they would not have dreamed of doing: tying themselves into tree tops as snipers, knowing they'd be killed, with no means of escape; lying in a pile of dead bodies waiting for a large enough group to pass by before detonating an explosive; gathering in a cave and committing mass suicide; suicidally charging (sometimes armed with only swords) against entrenched heavy machine guns; deploying into untenable positions; the list goes on. To combat this, US forces had to take a different approach. Bayonet bodies, just in case. When Japanese surrendered, which wasn't often, they often didn't make it to the rear. Few American soldiers and Marines were unfamiliar with how the Japanese treated their prisoners, and many were fine with somewhat returning the favor. With German POWs, they were generally trusted after surrendering. Some who were brought back to the US had many freedoms here, and enjoyed decent accommodations, even desiring to stay when the war ended. Meanwhile people of Japanese descent in America were put into internment camps for fear of their real "loyalties."

Culturally speaking, the less you understand of your enemy (language, religion, customs, or tactics), the easier in becomes to dehumanize them. The further down this path you go, the closer you get to things like souvenir hunting for teeth or other body parts (something we see happen often enough in the Pacific theater than it becomes associated with it). Heck there's even a Wiki page devoted specifically to this.

So, the theaters are generally depicted differently because they were fought differently. Even on a logistical scale, the fight in Europe might be taking one town, and moving across several miles of ground to engage the enemy again. In the Pacific, especially the Island-hopping campaigns, you might fight for a week to gain a single hillside.