Do you mean peer support group as in something like Alanon (AA/NA, whatever others there are)? I have gone to Alanon, but I've never done group therapy so I have nothing to compare...sorry.

In my experience with Alanon, it was more of a "share your experience" type of thing, rather than responding to someone's experience. Cross-talk is not allowed. I would imagine that in group therapy, you collaborate on ways to develop new coping skills by responding to other's stories or things they have shared, rather than just respectively listening and taking what you hear and trying to see how it fits with your life. The idea of Alanon was to realize you weren't alone in your situation, but nobody in the group can really go "Well here's what you should be doing" after you share your story. You can only share your personal experience, what worked and what didn't for you, and you try not to comment on anyone else's. Peer support groups like Alanon also do not have a facilitator, unlike group therapy where there is usually at least one psychologist or whatever there.