Both Chapter 7 and Chapter 13 discharge your personal liability for judgments in most cases. However, certain judgments are nondischargeable, like judgments for student loan debt, child support, alimony, most debts you owe to the government (like certain taxes or restitution in criminal cases), and awards for death or injury caused while driving under the influence of alcohol or drugs.
Most other judgment debt is dischargeable, but a creditor may file an objection to discharge in some cases, such as for injury caused by a malicious act like assault, fraud, or embezzlement. In Chapter 7, nondischargeable judgments "ride out" the bankruptcy, and you still owe them when your bankruptcy is finished. In Chapter 13, nondischargeable judgments may need to be paid through your bankruptcy plan. However, there are a few types of judgments that can be discharged in a Chapter 13 that cannot be discharged in a Chapter 7, so sometimes filing a Chapter 13 can be more advantageous than filing a Chapter 7. If you are concerned about whether your judgment debt is dischargeable in bankruptcy, talk to your bankruptcy attorney.