God knows what the history is now given the number of Crises we've had, but I'm assuming that the Spear of Destiny still prevented magic-based and supernatural heroes (like the Spectre and Dr. Fate) from entering Axis-occupied territory on New Earth, so history had to play out the same way it did (more or less) on Earth Prime.
Ditto in the Marvel Universe, since they didn't have anyone with Superman-level powers that could take on armies by themselves. Except that the Human Torch and Toro killed Hitler in his bunker.