Apples and mudskippers might be more accurate. The Apollo missions were telegraphed globally as a rallying call! The Manhattan Project was secret even after products were delivered and used!
Around 130,000 people worked on the MP. Perhaps 5-10,000 were security staff! 1,000 Military Police at Oak Ridge alone! Travel was restricted, communications were restricted, work was so well segregated that many project staff did not know what they had built until after the bombs were dropped! As VP, Truman did not know about the projects full scope!
The purpose of leaks for both projects are also different. Leaks from the MP would be detrimental to the country, war effort and world at large. Leaks from the Apollo project (with respect to exposing it was all faked and a waste of money) would have been to the benefit of the public by exposing fraud.
So no, he who thinks they can be compared, absolutely not!