And if all the players are playing at the same speed, it's not advantage nor disadvantage.
That's true, but it can still feel ****ty.
The LED is cool and all, but they are still triggers and games have different thresholds/deadzones (whatever you call it on a trigger) that might differ from that of the LED. So it's just another visual cue just as seeing him move his finger to press the trigger.
What he should measure (using a dedicated app and not a game!) is the delay of the signal from controller to console and the delay from the console to the monitor. Those are delays that every game ever made has and thus it's not relevant to discussing control-lag in console games.
The lag that is left over then still isn't the lag he wants to investigate because it still includes intentional delays.
E.g. adding time for the character to pull the trigger in-game makes the weapon seem heavier. So he needs developer input on what is intentional and what isn't.
The lag he now has is still not the lag he is after because he is still just looking at the animation not the inner working of the game.
In my opinion it's a lot simpler than all this testing makes it seem:
The delay of a decent monitor is negligible.
The delay of a decent controller is negligible.
The console doesn't add lag just because it's a console.
Games are capped at certain framerates and everyone knows VSync adds mouselag. The steadier (and higher!) your framerate is, the less mouselag you get.
If a game is capped at 60 and never dips below 60 it's not going to be noticeably laggy, especially since the controls by stick are more forgiving for this than a mouse.
If a game is capped at 60 fps but frequently drops below 60 it's going to be laggy but as the framerate is still pretty high it's not going to be too bad in most cases.
If a game is capped at 30 but it never dips below 30 it's going be less responsive than a 60 fps game because it only updates half as often, but it's not going to be laggy beyond that.
If a game is capped at 30 but barely runs at 30 it's going to be laggy and updates only half as fast as a 60 fps game and is closer to the really low framerates where it is percieved as "not smooth" so it's going to be pretty laggy.
In my opinion that's all there is to it. It's more noticeable on consoles than on PCs because everyone has the same hardware so if it's laggy for someone it's laggy for everyone. This makes it an issue of the game instead of an issue of someone's PC not being beefy enough.
It also makes it an everlasting issue because if it's laggy now it's going to be laggy forever, whereas on the PC it's going to play perfectly smooth after you sink some more money into your machine.