Yes. Competitively, imagine a scenario like this: an enemy is crossing a doorway in front of you, and that takes a tenth of a second. On 60hz, that gives you six frames to react. On 120hz, it gives you double that, 12 frames. Even though it's the same amount of time, a higher frame rate does indeed have an effect. (this can be seen a lot on 30 to 60hz as well. Usually players get better on higher frame rates.)