It's an interesting problem. Dry eye can often cause vision problems that are difficult to quantify (see recent abstract - I was just reading this yesterday - the full study is based on a literature search on the topic). I would guess it's related to surface irregularity from the poor tear film - though why exactly the Rx glasses would make that worse, hm, maybe the combination of surface irregularity from dryness plus the glasses somehow messes a little with your binocularity? That's just a wild amateur guess, but things like that have been known to happen amongst the LASIK crowd with corneal surface irrregularity for other reasons. (I'm a case in point.) I think that would jive with the contact lenses not presenting the same problem.
From my own experience back in my early days of eye problems I know it's not possible sometimes to draw a nice clean line between discomfort from dry eye and from eye strain. All very messy.
The Dry Eye Zone