Mark, as a matter of personal preference, I have never participated in any online crit groups. I have, however, been a member of several local groups, one of which I eventually became the group moderator for many years. The groups ranged from an old, established and honored group of both writers (of all genres - fiction and non-) and actors which has been around for close to forty years and still going strong, to a fairly new group which is still feeling its way through its scifi base. In-between are several others of varying stability and range.
Some groups focus on one particular specialty/genres, fiction, non-fiction, sci-fi, fantasy, thriller, etc. Others open their doors to all genres. Any successful group will have specific rules of conduct as far as crits and other commentary on others' writing. Some charge dues - which are generally used for a flower fund for ailing or celebrating members, or publishing an annual anthology of competitively submitted shorts, essays, etc. (the one group of which I was a member that had this setup charged a standard submission fee from which 1st, 2d, and 3d place winners were awarded cash prizes along with publication of their winning entries in the annual anthology. They regularly have submissions from around the country. Publication fees were paid out of annual membership dues.)
Some groups can be more social, while others are more businesslike. They may meet in a regular location such as a library or art gallery or they might be a 'traveling' guild that meets in a different place each week or month with pitch-in meals provided by the members.
The most important thing in any crit group is whether or not the members are all compatible. If they are not, there will be tension and attitude problems that can, if left unchecked, end up dismantling the entire group.