they both can have their advantages
but in certain cases that I find one better than other (and I'm only going to list some of the instances where IMO mf is better, duh

)
-wiping down your dash lint free (cotton lints white)
-wiping your instrument panel scratch free (cotton on clear plastic)
-wiping your wood trim, chrome trim and plastic
-cleaning interior windows and mirror (a spritz of water and 1 towel and it shines without chemicals lint free)
-mf towels can last for months and up to 300 washes if taken care of
-drying a car
-once you find a supplier you like it should remain consitant or comparable
-decreases chances of scratching during quick detailing
-dust pickup in general (use a cotton cloth and you need something like Pledge) use a mf and you don't even need water.
with any towel cotton or mf it's about quality and trying to keep the quality consistent, that's the most difficult part