Parenting: Family Meetings
It is interesting that you say you started family meetings as a way for the kids to air differences. If the kids see the family meeting as a complaint session, you will probably get a lot of defensiveness and competition. Kids may even save up issues to throw out at the next meeting. The best approach to planning family meetings is probably to set up the expectation that the whole family will meet to try to make decisions and solve problems together.
When children have a conflict going, family meetings can be a good time to try to help them understand each other and find a solution they and the whole family can live with. Parents can serve as mediators, giving each child a turn to explain his or her feelings and concerns. The first child to talk should be able to explain until the other child can restate his or her sibling's concerns accurately without judging whether those feelings are valid or not. Then the second child should have a chance to talk and explain how he or she feels. The goal of this first step is simply achieving understanding in both siblings.
If there is still a conflict after the siblings understand the feelings of the other, then the siblings can start brainstorming solutions. If it is a problem that affects everyone in the family meeting, everyone could share feelings and suggest solutions. All solutions should count and should be recorded. Even silly ones should be written down. Then the family as a whole can start going through the list and marking off solutions that are not possible and adding support for the ones they like. Through a give-and-take discussion a solution can be chosen, maybe through a vote, and plans should be made to enact it. Rather than considering that the end point, a time should be set to talk about the issue again to see if the solution is working. When you look at the situation again, you may decide you need to try something else. If so, the process can begin again.
Some recommendations are available online for organizing and conducting family meetings.