In my experiments it depends on what the bow/arrow combination tells me it needs.
All other things being equal, the harder plate (leather) will move the arrow impact away from the side that the sight window is on. So, for a right-handed shooter, a harder plate would move the arrow impact a bit left -- and a softer plate would move the impact right.
Now, that is the result of my experiments. You might get different results. I do think that experimenting is worth the time it takes. Little things can make big differences.