I think it really depends on where you are credit wise as far as making the decision to go with CCC. Frankly if you are totally behind in your bills, I'm talking late/no pays so your credit is already looking bad then CCC is probably not a bad thing. It will help you pay the bills off and any impact on your credit will be minimum since your credit is not good.
I think using CCC becomes dicier where you are making the payments and your credit is still looking good but you want to reduce payments. For starters as I learned they don't reduce the payments, just the interest.
Frankly for what they do if you are in good standing with your creditors you can all and try to negotiate on your own.
Personally I find their services questionable. I recently called them and talked to a counselor who based off my bills/debts came up with a payment amount that was more than the amount of money I had.
When I questioned the counselor on how she thought me paying X amount on my income was feasible she admitted that their formula did not take my living bills or income into consideration, just my debt and what the costs would be of paying the debt off in X amount of years with a lowered interest rate. Considering that if I went with CCC, I should not obtain additional credit, a debt repayment plan that leaves no extra money for emergencies (car break down, etc) does not seem like sound financial management to me.