Freer societies tend to have better technology as they are much better at allowing people to reach their full potential, develop technologies, etc, so even though the Greater Axis has much larger resources and populations, that will give them the advantage only in the short term.
For civillian use perhaps, and maybe that's the winner at the end of the day. But in military terms authoritarian regimes are just as capable in fact possibly even more so as they're generally focused on repression and 'hard' power, whose greatest institution is of course the military.
Read Elizabeth Chua's "Day of Empire" and consider that, thanks to the Nazis, the U.S. got the Jewish nuclear scientists and thus the atomic bomb while the Nazis kept going down dead ends. The only way it could be more ironic is if the war in Europe lasted longer and Nuremberg or Munich got nuked.
I'd wager that the funds, resources and excellent organisational skills the Americans could and chose to access outweighed the benefits of European refugees. Not that they weren't important but give Kurt Diebner's team a centralised, well funded A-bomb production project and Oppenheimer's team a poorly funded, bureaucratic nightmare (or any other of the several German projects or think tanks or debating societies that where going on at the time) and see who gets the bomb first.
The Soviet Union is an excellent example of a totalitarian state that managed to get the bomb thanks to it's own home grown talent when the project was well funded and well organised, except they, unlike the Americans had to undergo four years of the worst conflict in human history beforehand.
"Oceania" may continue to develop where Eurasia eventually stagnates under a gigantic totalitarian "dead hand."
It's something of a gamble, either Oceania can't properly advance without essentially finlandising itself to Eurasia, a nation that essentially degenerates into poverty or instability through it's isolation, or a technological powerhouse which leaves the silly deadlock of earth to expand through the solar system and then on, leaving Eurasia plodding along.