It mostly has to do with the fact that FPSs can get away with a lot of techniques in an effort to hide lag. Anyone who has played old school Counter-Strike will attest to the phenomenon of dodging behind a wall and all of a sudden, you die.
It’s referred to as “Client Side Prediction”, where your computer will make its best guess as to the outcome of any action you do, and will correct itself once the server sends a message back with the true results. In an FPS, such corrections are usually minor and go unnoticed, where as a fighter, you get the proverbial “rollback” effect.
In the end, lag is just easier to hide in an FPS than in fighters, but it is still there. Even with the best netcode in the world, lag will always be present to a certain degree. All that will matter is distance. Network speed is limited by the speed of light, meaning it’s pretty much impossible to have a truly “lagless” experience with people over a great distance.