I guess you'd get cleaner with a washcloth as it has more surface area contacting your skin and may be a bit more abrasive. Most of the "dirt" is dead skin, so you'll want to get that off to feel clean. Your mother is pretty smart.
The dirt you find on the washcloth is trapped in the material. The dirt on your hands would be quickly rinsed off.
I don't use a washcloth in the shower, but like to use one in the tub. I particularly wouldn't use one while washing my sweetie for reasons other than cleanliness.
