I'm sure Richard will have more to add, but here is what I know.
Tapered gibs bear against both surfaces over their full length because of the way they adjust. this means even pressure over the length of the slide. They are also easier to adjust because you typically have a single adjusting screw (and a stop screw). With parallel gibs they are typically adjusted (is there any other way to adjust this type, I have never seen one...) by using set screws to apply pressure to the gib strip. This creates pressure points where the screws contact. You tend to get uneven wear, and the gib strip doesn't bear evenly.
Parallel gibs do work, I had them on my first lathe, and first mill. Both my current machines have tapered gibs, and I think it's definitely an improvement in design.