How costly an invasion of Japan might have become

Would an invasion of Japan have been bloodier than the fighting in Europe?

It likely would have resembled the Eastern Front in Europe more than the Western Front campaign.

An invasion of Japan is compared with the intensity and human cost of the Eastern Front rather than the fighting in Western Europe. The home-island campaign would combine amphibious assault with a much larger and more sustained land war. That prospect explains why planners treated theatre-specific retraining and enormous logistics preparation so seriously.