I tend to side with wash cloths. Typically when a wash cloth gets dirty you wash it in the washing machine. With sponges, though, you don't do that. Until you replace the sponge entirely, for the most part it just sits there and collects tons and TONS of bacteria. This, I find gross.
Unless you can find a reusable sponge -- yuck. xD
Sponges harbor a LOT of bacteria. The best thing are actually those special dish scrubbies with the fillable handle for the dish soap. They are much more washable because of the plastic like bristles. Dish Clothes are just the same, unless you use a new one every time you do dishes, but they dont offer much scrubbing power.
I prefer to use sponges, as they seem to clean better... and are easier to use. I was concerned about the bacteria that sponges collect... but you can disinfect them, like so - http://www.funadvice.com/tip/spongesfreebacteria_microwaving wash cloths don't seem to clean too well, and it takes more effort.
Sponges with the scrubby side so u have a little extra power to scrub, just b sure to clean them good and replace them when they need it
Umm sponges to wash and dish rags to dry.sponges usually have a hard side to get off grease and grime.
sponges are more clean