Why such a narrow focus on FPS games? Controllers are superior imo for a far wider range of games where analogue control is beneficial. Especially third person games, one example would be trying to control the horse on red Dead redemption 2 with digital keyboard controls, it's like playing a game from 1980, same goes for games that use keyboard for controlling vehicles. Actually anything that requires more finese than digital inputs can provide.
I agree mouse is superior for FPS games because they make it so easy. I'm sure people would choose PC gaming because it also has a wider selection for peripherals for games like racing Sims, flight Sims and it can just as well use flight sticks. Trying to narrow down the choice between the two because of a specific gaming genre isn't going to work, because PC can cater for all of it for starters.
I play a few games that I can't imagine would work (or are available on console) as they require too many inputs but even games like Diablo3 I preferred using a controller, game by game basis I guess.
On another note, I'd take suffering a controller for an FPS over the excessive amount of cheating that goes on in PC multiplayer titles any day of the week.