Reegar gains shots at higher FPS. I'm refering to visually though. At a high enough FPS your brains starts to ignore frames because it can't process them fast enough.
Your eyes / brain don't see in "frames per second" it sees a constant undending stream of information. The length of time each "frame" or picture is displayed for dictates how easily the brain can interpret what it is seeing as motion/ fluidity.
Personally speaking, there is a difference between 100fps and 144, not just in terms of control but in terms of smoothness.
Your brain can see and doesn't like it when parts of animations are missed out.
Your brain doesn't "ignore" frames, it simply processes them with the same ms delays that it processes everything else. I could run some shootmania replays, and slow them down to 1/4 of normal speed. You'd be surprised just how much more you can see with 60 instead of 30, or with 120 instead of 60. And your brain subconsciously picks up that parts of what it's seeing are missing; 120 for fast gaming is about the only way that stuff will look truly fluid.
The brain doesn't "miss" information IRL: when something changes position quickly, so why would it miss processing that information in the context of pictures on a screen? Just because you can't pick out each individual picture, doesn't mean you're not acknowledging that they're being shown; your brain doesn't think anything of it when it sees something move in a life like motion, with no blurring and no "missing" chunks. It can however detect low dps very easily.
I can't watch movies on my monitor up close, otherwise I can see the stuttering in the film, where a frame is displayed for 5x longer than I'm used to it being displayed for.