There were a number of pros and cons to the Space Race. Some had to do with geopolitics while others had to do with technology. Some are clearly tangible while others are not.
The biggest benefit is one that may or may not really exist. This is the benefit that the US received from winning the Cold War. It is clearly a good thing that the US won the Cold War. The Soviet communist system was clearly repressive and was a system that did not give its people either economic prosperity or personal freedom. We are much better off for the fact that communism did not come to dominate the world. The Space Race might have had something to do with that. US development of missiles that could carry nuclear weapons may have helped deter Soviet military aggression. The Space Race may have caused the Soviets to spend too much on their military, thus making them less able to provide consumer goods for their people. If the Space Race helped us win the Cold War, that would be a major benefit.
A second benefit of the Space Race that is more clearly tangible but perhaps less important is the fact that the Space Race caused advances in science and technology. These advances have helped to improve our economy and to make our lives easier. This is another clear benefit.
The main con of the Space Race is, arguably, that it wasted money. We can argue that the US would not really have needed to spend all that money on such things as putting people on the moon. This was not something that helped the US tremendously and the benefits might have been achievable at a much lower cost.