I hitch the way Wulff did with the hitch coming off the bank side of the fly when the fly is pointed downstream. I do so because first that was how I learned how to do it from Wulff's writings on the hitch. Secondly I do so because it gets the fly up and riffling a little higher than Lee's method of putting the hitch on the opposite side of the bank when the fly is facing downstream.
As far as where the fish is hooked, I found most of them are hooked in the right side of the jaw when fishing right bank and left side when fishing left bank.
I know Lee says you have a better chance at a solid hookup with his opposite side method because the fish simply turns downstream after picking up the riffled fly. This would put the hook in the left jaw on river right and the right jaw on river left. Maybe so, but by putting the hitch on the opposite side like Lee advocates, the fish should be hooked in the opposite jaw from the river side you are fishing simply because that is the way the hook point is angled.
Therefore, I've come to the conclusion several years ago that hooking effectiveness isn't really any different with either method of placing the hitch, and that the most important thing is getting the fly up and swimming erratically as soon as possible. Since Wulff's method gets the fly up a little faster, helps keep the fly from drowning because the hitch is always pulling the hook eye up (whereas Lee's hitch is always pulling the hook eye down a bit), and keeping the fly broadside for the largest profile is most important to me, I use Wulff's method.
As far as putting the hitch on the bottom of the fly, it certainly works and keeps the fly riding high; but the fly doesn't have nearly as large a profile when the hitch is under the eye and not on either side. And since the only wets I use a hitch on are low-water wets, I want as large a profile as I can get. I also use the hitch with a bomber (I never fish a bomber without a hitch) to keep it up and swimming erratically all the way across the river.