Actually the Germans developed the theory that the US exploited. It's just that by the time of WW2, the NAZI's had chased the researchers to the US.
What they lagged on was the engineering expertise to put the theories into practice. The US spent billions to develop this expertise in a short period. The Nazis simply did not have the resources to spend on this development. What little they put aside for new weapons development was spent on jet fighters and the V1/V2 missiles.
They were not even close to developing an A bomb. They had no equipment for seperating U235 on an industrial scale, no reactors for plutonium production, no research facilities for determining the critical masses necessary (interesting stories from Los Alamos on "tickling the tiger" from a physics prof I had), etc.
When you look at the ten reasons the Germans lost the war...chasing the jewish scientists and university professors out of Germany ranks near the top. They basically gave up on 50 percent of their national brainpower. Just paint the picture with Einstein and all of the Jewish scientists still in Germany and the Holocost never occurring...and you start to have major changes in the outcome of the war.