Were they these same (APxx 1604) inserts or something different? I have to think the pockets themselves control 99% of the insert height relative to cutting plan datum. Maybe there is a way you can get a DTI in the top corner of each pocket to compare. If that checks out, then maybe the screw hole is low & drawing the insert down? (but you would visibly see a gap on top of insert).
Just a thought, have you calipered the inserts themselves to see if they are identical? If for example you had different nose radii other geometric feature, would that account for different contact height? I really don't know how these are designed. Maybe the contact position is supposed to be identical. Or maybe the parallelogram is the same but a larger nose radius would effectively shorten the height?