What does biodegradable mean? Well by definition it means capable of being decomposed by biological agents like bacteria. Materials are usually deemed biodegradable if they break down to at least 90% h2O, CO2 and biomass within 6 months, although some materials may take years to biodegrade. Keep in mind that biodegradability doesn't necessarily mean environmentally friendly.
I don't use any soap whatsoever when backpacking. Washcloths work great. I prefer to keep chemicals out of the backcounty. For me this includes insect repellents and deodorant. My philosophy is that if I wouldn't want to drink it then I won't use it. I wouldn't appreciate it if chemicals washed off somebody washing upstream while I'm filtering water downstream. I swim a lot, so since I don't want to drink chemicals I wouldn't want to contaminate the water for anyone else.
Guess where I do use biodegradable soap? I use it at home instead of regular detergents. Hey I try to be "green" and lessen my environmental footprint any way I can.