I have both and I find the shag super, super plush and soft and sucks moisture right up. The microfiber feels a lot more rigid to me somehow and I can hear the crinkly middle absorbent portion more too.
I only have the microfiber, but from what I have read, the shag is somewhat more absorbent because of the thicker "furry" material. However, either will do the job of protecting your bed from fluids. I love my microfiber throe!