There's been extensive study into the latency difference between 360 controllers and ps3 controllers. There is virtually none and it's definitely not noticeable with all the other latency sources in the signal chain.
You might be surprised to discover that the radio waves don't care if they're going to a desktop PC in a traditional case, or a slightly different desktop PC in a Microsoft/Sony case!
It was not "the common perception". At best it was common among your peer group?
Edit: one public, easy to digest source
https://www.reddit.com/r/RocketLeague/comments/8wvf9u/contro...