Going from 60hz to 120hz was a big difference. Going from 120hz to 240hz was not a big change, but definitely better.
So my bet is you actually will see a change and feel the change, but it won't be a very significant change from 240 to 360hz.
If I had a 120hz/144hz screen and mainly played for example CS:GO, at a higher level, I would probably upgrade to a 360hz screen, unless the price is completely bonkers.