My husband had a DUI conviction (no harm to property or persons) in 2006 and successfully applied for a B-2 tourist visa to visit the US in 2008. There have been no convictions since. The ESTA eligibility questions have now changed and he is able to answer 'no' to them all. Would he now be able to apply for an ESTA without the need to apply for another visa? (it was an extremely long and expensive process!)
I assume that your husband disclosed his conviction in his earlier B-2 visa application. Because he was already issued a B visa and admitted to the US with this conviction, you can conclude that the conviction does not make him inadmissible to the US.
The statutory requirements for admission under the VWP do not go very far beyond those for a B visa, and nothing you've said suggests that he would fail to meet any of these additional requirements. Therefore, your husband should apply for ESTA authorization and, if it is granted, use it.
If ESTA authorization is not granted, he will need to apply for a visa, but if he doesn't apply for ESTA, he'll certainly have to apply for a visa, so he might as well try.