This is a good question. In my opinion, the two options are for two totally different financial situations. Dave Ramsey preaches a method of paying the debt with the lowest balance off first while simultaneously making minimum payments on your other debts until the debts are paid off in full. Once the lowest balance debt is paid then he suggests you move on to the next lowest balance, etc…etc… (you can read a more detailed description and analysis of this on this debt blog).
Dave Ramsey’s approach assumes you CAN AFFORD to make the minimum payment due on all you debts AND make MORE THAN the minimum payment on your debt with the lowest balance (interest + principle in order to pay down the balance aggressively).
What if this is not the case? Most people who should consider debt settlement are those who CANNOT AFFORD to pay off much, if any, of the principle on ANY of their debt. In other words, they are in way over their heads and the debt has spiraled out of control. With all the high interest rates, fees, and late payment penalties kicking in, they can barely even make the minimum payments each month. Once this occurs, it is hard to stop even if you stop spending and cut up your credit cards.
So, yes, Dave Ramsey’s approach is a great help for many people who have not yet reached the tipping point and it is always better to try and pay off all your debts through strict budgeting. However, for those who have passed that point, that is when debt settlement can help assuming one understands all the benefits and risks that go alone with the debt settlement process.