Open vs. Closed Fingering... Tuning Issues

I have two chanters: A Daye penny chanter which plays in tune for both octaves with open or closed fingering, and an expensive chanter from a current maker which plays horribly flat in the second octave with open fingering and in tune with closed fingering.
I’m wondering if the differences are reed-related, or if most folks use closed fingering anyway and thus don’t have to deal with this. (By way of explanation, I learned the whistles first, so am now re-learning fingering for the pipes.)

Bob in Wheaton IL