They're about the same height.
60% of 170 mm = 102 mm
55% of 180 mm = 99 mm
So the 170 will turn in faster, with its narrower width and tighter curve radius.
Well, he said he had the 180 previously, and just replaced it with manufacturers recommended size of the 170. So he will soon have direct experience with both and be able to decide for himself. He's just having some doubts because some of the local guys think they know better than the engineers who designed it what tire it needs. (Probably the same guys who would tell him to "break it in hard, like a racebike".) I certainly think it would be silly to get rid of his new tire and put a 180 back on; it's not going to be that huge a difference. If he decides he likes the 180 more he can switch back on his next tire.
But for any canyon carving, he's better off with the 170. He would only need the 180 if he has modified it for significantly increased power, or maybe if he's dragracing.
PhilB