It's all about angles.

Assuming that you use a knot that either grips the hook eye or a loop knot, then:

It will make a diference in the how the fly is pulled through the water. It will make a difference on how the force of a hookset is applied to the hook point. It will make a difference in how the fly rides in the water.

Will that difference be obvious or detrimental to your fishing? Who knows? All the differences (except one) will be slight to the point of likely irrelevance. But, if you believe it matters, then it probably does.

The only easily obvious difference between hook eye location will be it's effect on how the fly rides in the water. And this requires a couple of dressing details to fall in line before it occurs. If, in tying the fly, the weight of the dressing above the place on the hook eye where the line exerts it's force weighs more than the portion of the hook bend and point that hangs below that point, then a down eye hook will cause the fly to ride upside down. This is primarily because the point of pull on the fly is also below the hook shank. This puts the hook shank's weight into the equation, making it more likely for the hook to flip in the water. Not always a bad thing. I like many of my flies to ride hook point up, less snags and I like hooking fish in the top of the lip.

Also, as you look at the angle of the hook eye, you'd think that the line would pull up on an up eyed hook, down on a down eye hook, and straight on a straight eye hook. That only applies if the line of pull is straight. Then, the angle of hook eye will act as minimal planing surface or lip, and have a very slight effect on which direction the fly moves. It would be hard to see this with a naked eye. Different shapes and materials in the fly's dressing would also effect this, probably more than the hook eye direction.

The direction of pull will always follow the line, unless you build into your fly some kind of lip, plane, or excentric to cause it to have it's own action. If the line is pulling from above the fly, the fly will go up when pulled, regardless of the hook eye angle. Same with down.

Again, any movement or action imparted to the fly itself by the hook eye angle will be really really slight.

It still matters, though, if you believe it does.

Buddy