I could even see the Nazis trying to regain their firearms toehold and make basic black powder weapons (if they exist or the basic components do).
I was thinking the same, myself.
Initially, their superior firepower gives them a huge advantage
What advantage? My wand of fireball trumps your weeny pistol!
It would depend on the size & nature of the Nazi force making the trip.
Even in WWII, the tech for attacking over the horizon existed, and no wizard out there could envision attacking from 30,000+ feet in the air. Once the Nazis realized what was going on, any wizard who wasn't paying attention would hear a mysterious whistle and then their world would light up with a fireball bigger than they'd ever seen...one that would pierce their tower walls, to boot.
While less maneuverable, little in the fantasy realm could match the speed of some Messerschmitts 400mph bombing/strafing runs.
And all that assumes that the arcane Nazi rituals that didn't quite work in the RW continued to be ineffective in the fantasy realm. What if those Nazi SS "Warlocks" suddenly found their spells effective at raising an army of undead?
(BTW, check out Harry Turtledove's
Darkness series for a very interesting take on what a fantasy version of the Nazi's Final Solution could look like. Can you say Necromancy?)
A small force of Nazis seeking the Spear of Destiny accidentally rip a hole in time & space, winding up in a fantasy world.
Why aren't they looking for the Holy Grail?
According to what I've read, they were looking for the Spear of Destiny and any other legendary relic or artifact they could find to strengthen their armies. So it could be the Holy Grail or anything else that captures your fancy.
Have the fey decide they liked the world better when it was...less populated.
Dude! I'm using something like that in my current campaign W.I.P.! Only, in my world, there has been a huge extinction level event, and there are forces trying to prevent the resurgence of civilization.