On a bare hook a down eye reduces the hook gape, when compared to the same size/model hook with a straight or ring eye, or an up eye.
However... on a finished pattern I would be hard pushed to come up with more than a small handfull of patterns where the _thorax_ bulk, not the hook eye, limiting factor. As such the argument in favor of up eye or ring eye based on effective hook gape would appear to me a moot one at best.
leaving in the early morning for a week fishing in Slovenia. I may even fish some flies tied on very small hooks. Down eye ones, of course
=== You have a friend in Low Places ===