I always thought this is a rule of thumb, but then I learned that wireless gamepads for popular consoles (back then it was PS3/PS4 era) don't really follow that pattern. I came across multiple tests where older wireless PS controllers and xbox controllers were consistently more responsive in practice.

For modern ones there are some cool posts like this one [1], where most of the time there "were no statistically significant difference", or even wireless was more responsive.

Gamepads always impressed me - they can deliver insanely good response times while streaming high quality audio with no lag. I never found other BT accessories for phones/computers that were even close to that smooth experience.

[1] https://www.reddit.com/r/PS5/comments/m020e3/dualsense_wired...