Arguably the most controversial choice on our list, The Godfather Part 2 isn't necessarily an improvement, it's almost a completely different, but equally excellent, film. While the first Godfather introduced us to the Corleone Family and its inner workings, Part 2 showed audiences its humble beginnings and future. Where one has Brando, the other has DeNiro, and where one has "I'm gonna make him an offer he can't refuse," the other has "I know it was you Fredo."
It's basically comparing two masterpieces, but there are some out there who prefer Part 2 to the first and suggest director Francis Ford Coppola found a better overall approach with the second film. But, in all honesty, you can't go wrong with either of the first two Godfather films, as both are Best Picture Oscar winners. But, you're better served avoiding the third.