Von Braun and Korolev in America

Sergei Korolev was imprisoned in the Soviet Union in 1938. Suppose he escapes to America. Wernher von Braun, meanwhile, had a much more positive relationship with his government during the 30s. But suppose he also ended up with politically connected enemies and was in danger in Germany, and also flees his country, for America.

How does rocketry advance in a scenario in which two of the leading visionaries of the era are working in the same country, likely together? I imagine they'd be roped into the war effort, but for a much less brutal government than either Nazi Germany or Soviet Russia. This could result in the allies having more sophisticated rockets than the Germans, which would likely alter the war to some degree, but not drastically so. Meanwhile, what does the US space program look like in this scenario? Do we just shave off a year or two on the various milestones?
 
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