Strict punishments for criminals is more important than gun control, Barbour said.
"We should punish people who commit crimes with guns. Dole says we don't need the Brady bill. All we need is a system of instant checks," to prevent convicts from purchasing guns.
Dodd replied that the Clinton-backed Brady bill, which imposes waiting periods for handgun purchases, has helped reduce the nation's crime rate by 9 percent.
The speakers also clashed over affirmative action.
Both speakers concluded the 90-minute event by asking the audience to make an informed decision, based in major issues, and Barbour stuck to his guns.
"Issues and ideas are what shape America," he said. "I ask you to make the decision based on facts and not based on misstatements of facts."