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A Chapter 7 Bankruptcy is preferable to a Chapter 13, because with a Chapter 7 you don't pay your unsecured creditors anything, and with a Chapter 13 you have to pay all disposable income (after subtracting allowable expenses) for 5 years.
However, to get rid of a second mortgage, you have to file a Chapter 13. Filing a Chapter 13 can also reduce the amount that you have to pay to unsecured creditors.