"Operation Barbarossa", was not a "battle", it was Germany's champaign against the Soviet Union. It included many battles. Of the battles in the European Theater of Operations that was most decisive in the defeat of Germany, it is arguably the battle of Kursk. There were more men and tanks in this battle than any other in the war. It should be remembered that
80% of the entire German war materials, men, tanks, guns, and war efforts were expended in the East (Soviet Union).
But do not take my word for it, the research is easy to find, just search on the Battle of Kursk, the battle of Stalingrad,
Of the major battles in the west, the Normandy landing had fewer allied casualties than the battle of Market Garden. The most American blood was likely spilled in the Battle of Hürtgen Forest (A battle the most Americans never have heard of.). The most significant battles in terms size and blood were Hürtgen Forest and the Battle of the Bulge.
Never the less, the significance of the Normandy Landing was the gaining a foot hold on the European Continent, not the numbers of troops (not on day one anyway), or the casualties.
Monte Casino was very bloody also, but its military significance was most likely just as a means of diverting German troops from the Eastern Front, and from garrisoning the Atlantic Wall.
However, do the research and look at the resources expended and casualties, you will see that the in Europe, WWII was mainly fought in the East. Few, if any of the battles in the West could match the amounts of committed resources and the number of casualties on both sides. Germany was bled white in the East.
http://en.wikipedia.org/wiki/Battle_of_Kursk
From the above link:
German strength:
780900 men
2,928 tanks, 9966 guns and mortars.
2110 aircraft
Soviet Union strength:
1,910, 361 men
5,128 tanks
26,013 guns and mortars
2, 792 aircraft
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Germans:
203,000 Casualties
720 destroyed tanks and assault guns.
681 destroyed aircraft
Soviet Union:
863,303 Casualties
6064 Tanks and assault guns destroyed.
1626 destroyed aircraft