The keyboard and mouse versus controller argument is usually conducted as a matter of taste, and it is much closer to a question of what kind of game you are playing. Some genres are effectively unplayable on one and some are unplayable on the other, and the crossover is narrower than the discourse suggests.
Where mouse and keyboard wins outright
Real-time strategy, city builders, grand strategy, and any game where you are selecting a group of units and issuing a compound order. The advantage is not reflexes, it is that you can issue several commands to several targets in one motion without losing the main character's position on screen.
It also wins for anything involving inventory management at speed and for games with a high unit count where individual unit control matters.
Where controller wins outright
Third-person action games, especially the ones built around a lock-on camera. A controller's analog stick is a genuinely different input model from a mouse, and games designed around analog movement do not translate cleanly to keyboard movement.
It also wins for fighting games and for anything where you hold multiple buttons in combination while moving. Fighting game inputs are designed around a controller's face button layout and are particularly painful to map to a keyboard.
Where it genuinely does not matter
Most strategy games at a slower pace, most RPGs without action combat, most puzzle games, and most simulation games where you are clicking on things rather than aiming. The community arguing about this is arguing about the small slice where it does matter.
The practical middle ground
A game that supports both does not necessarily balance them evenly, and the difference is usually in the aim assist or aim magnetism. Console versions of a PC game carry aim assist by default because the hardware requires it. Playing the PC version with a controller usually gives you a controller without the console assist, which is a meaningfully worse experience and probably the single most common source of frustration for people trying to play a PC game with a gamepad.