Hi Alan
What appears to be the 'Ladies' favourite, Multifilament Poly, is certainly easy on the hands but as the yarns which in turn are wound into the strands (3 per rope - in most cases) are made up from very fine filaments (this is why it's so smooth) it is very easily prone to wear & tear. Just imagine pulling a fine piece of sand paper across your hair, it's going to catch on every one it touches. Doing the same on a lot thicker hair would be less pronounced.
To help reduce any discomfort to your hands try to adopt this:-
When paying out or hauling the rope avoid letting it slip through your hands. Grip the rope and move it from hand to hand. Old habits are always hard to break but allowing rope to slip through your hands can have the effect of sanding your skin.
Monofilament Poly is better than splitfilm, more durable although a little stiffer to coil but easier on the hands. As the name suggests it is made up from numerous filaments of round poly. Think of a fishing line, now think of lots of them in a bunch and then wound into a strand.
Smooth to the touch, reasonable performance and cost effective.
Don't forget to air dry your ropes whenever possible, keep out of direct sunlight when not in use & visually check regularly.
Hope this helps a little
Clivo