It’s two different approaches to the moon.

The Americans’ F-1 rocket engine that powered the Apollo flights was truly impressive, and remains one of the most powerful single combustion rocket engine ever made. However, they were gas generator engines that are highly inefficient, which is why today you won’t see the Americans trying to go to the moon using the same design.

The Soviet N1 moon rocket was instead powered by 30 small but far more efficient NK-15 engines. The problem for them was that the computer system used at the time (KORD) was not responsive enough to react to multiple rapidly occurring processes and which led to faulty controls during launch.

To put it another way, the Americans strapped on the bigger but less efficient rocket engines and got lucky. The Soviets tried a novel and innovative design that was way ahead of their time and failed.

However, the Soviets shall get the last laugh, because 50 years later the American SpaceX company would copy the same concept for their super heavy lift vehicle design (Super Heavy used for Starship), which in many ways conceded that the Soviet design was a more viable one.

On the left: N-1 (1969-72), on the right: SpaceX Super Heavy (April 2022, which exploded during the test launch)

Reminder that even 50 years later, SpaceX Starship also experienced failure during its first orbital test flight despite advances in technology and especially leaps in computing power.