I think the neo-Nazi guerilla movement would have been less likely to spring up after WWII. By "allowing" the Allies to capture him and eventually execute him, he became a martyr and a cause celebre for those who didn't want to abandon the fight. Hitler dying by his own hand wouldn't have galvanized the die-hard partisans.
It would have been more likely that Germany would be stable and unified in the aftermath of WWII, and there wouldn't have been the fighting between the neo-Nazi guerillas, the communists, and the proponents of democracy.