I think if you want a fly to skitter, an upturned hook works best. Also on a small fly, this opens the gap of the hook a bit. Well it keeps the eye out of the way, anyhow. It also better for certain knots, such as snelling the hook or using a turle knot.
A downturned eye is supposed to be better for setting the hook. It is also a good profile for emergers.
A straight eye is sort of the default. It makes a nice profile with the tippet on most flies.
That's my $0.02.