Warren,

As are most things in fly fishing (I'm sure you know that), it depends on who you ask. I'll get to that shortly. Different types of eyes on fly tying hooks: TDE, TUE, Straight Eye, Looped TUE, Looped TDE, and No eyes(for snelled flies). I may have even missed 1.
WHY : Some writers consider the angle of the pull of the point important and the direction of the eye a key to that angle. Maybe yes, maybe no. Some prefer the 'look' of a fly tied on one or the other. The 'looped' eye does not have anything rough on which to cut the tippet so it's more secure but added wire results in a heavier hook. These are used mostly for wets/nymphs and streamers although in xfine wire can be used for low water salmon flies. The eyeless hook is 'classical'. The manufacturers, at least some of them, offer choices. Then we select what we do based on how we've been influenced and what's available.
I've never measured the shank length of say a Mustad 94840 TDE and a 94842 TUE in the same size but I 'think' or I've heard that the TDE offers a tad bit more tying length. Not sure if that's true. On the tiny stuff, 24 and smaller, I think that a lot of tyers prefer the staright eye.
Have I cleared this up? LOL.

Allan