it matters less at D II. I think everyone agrees on that. No one really agrees on what the prestige values mean at D I (there are accepted "ranges") and no one really agrees on how much less it matters in D II, but it does matter less. Someone will say that it really doesn't matter less, just that the money involved is smaller at D II and therefore the effect is felt less, but ultimately that means the same thing just by different means.
Distance and number of ships then maybe postseason money all matter at least as much as prestige at D II IMO. If I have an advantage in 2 or 3 of those, prestige won't necessarily keep me from battle, especially if I can't find an alternative that I like.