I don't think the German "soldier" was better or braver on average.
Better trained, more disciplined, and better equipped. Their only problem was that there were too few of them, thankfully. They inflicted massive casualties on opposing armies. They just outran their supply lines and faced an enemy, the Soviets, who accepted an horrendous loss of life to achieve their objectives. It became a battle of attrition.
Most Americans believe that D-Day was the pivotal battle of the war, but Kursk was the downfall of the German military. It should be noted that British intelligence was able to discover the German plans for Kursk and informed the Soviets prior to the battle. I still have difficulty comprehending the size and scope of Kursk. The statistics are mind-boggling.
Losing an entire Army at Stalingrad because the idiotic decisions of a Corporal was a major blow as well.