In mathematics, when something is a factor 4 better/worse, does it mean that compared with something else, it is 4 times larger in value.
Hope that's clear.
Purely on a semantical point - and I'm not disagreeing with your answer, but if, say, a box of cornflakes contains 1kg of cornflakes, then a box that contains 4 times as many would contain 4kg, right? But would a box that contains 4 times more contain 5kg?
That is what I would say. "Four times as much" is 4x. "Four times more" is x+ 4x= 5x.
Of course, I have no idea which of those "factor 4 better/worse" is supposed to mean!
(Oh, and "4 more or less" is .)