The Zanio system also has a preference. Sal Zanio recommends that you go out to bed Bath & Beyond and spend your last paycheck by getting some high count Egyptian cotton terry cloth towels for work with his chemical system. (He has a whole chapter on the care and maintenance of these towels once they get into service.)
It is my understanding that the microfiber cloths and mitts are made from varying-quality, probably recycled, plastic products. As such, it makes sense that rubbing your car down with a piece of plastic will do damage to you finish.
Personally, I can't tell the difference between a car detailed with cotton and one detailed with microfiber. But, down the road, after a number of years, how much of the original finish is going to be remaining if it has been continually rubbed down with a manufactured synthetic cloth?
http://www.zainostore.com/mm5/merchant.mvc?Screen=towel_guidelines&Store_Code=Z
Bill K