How would the level of brutality in a potential invasion of Japan compare to that of the Allied invasion of Germany?

 The Japanese were clearly less willing to surrender than the Germans. The average German in 1945 offered little to no resistance to the advancing Allied troops (mainly the Western Allies; they were harder on the Soviets after hearing all the stories from fleeing refugees). Many unit commanders, especially the Volkssturm militia, did the sensible thing and gave up without a fight rather than waste the lives of those they were in charge of.

On the other hand, Japanese resistance was always brutal. They saw the Allied soldiers the same way like how the Germans saw the Soviets, except worse. To add to that, the country had been under the military junta for decades and much of the population had been indoctrinated into obedience through their education system. In Okinawa, the Japanese casualties was nearly total, with less than 10% of their forces surrendering; like in many previous battles, the soldiers were told that they could expect no quarter from the Americans so many of them just never surrendered. They also saw no problem in conscripting young boys, even if they’re mostly for auxiliary roles.

There’s every reason to expect that the invasion of Japan would be no different, except on a much larger scale. Since the Japanese were running low on trained soldiers, they prepared numerous kamikaze-like units, for example the Fukuryu living sea mine/divers.

To make it worse, the Japanese correctly deduced the Allied landing sites because there were so few of them to begin with. The initial landings might make Omaha Beach look like a picnic and it won’t get much better from there—the projected 1 million+ casualties on the Allied side might be correct and the Japanese side might be many times worse.