First of all, I point the reader to my post on workshop structure, and the comment thread which follows it.
That being said, it's safe to say that writing groups are highly idiosyncratic. The relationship between a writer and a group is also highly dynamic, dependent on the writer's career state and the group's state in its life cycle. Groups are also susceptible to the effect of strong personalities, even absent any attempted coup.
While all of the above are true of many social organizations, with writers groups these tendencies seem to be magnified.
Let me go to specifics. A newer writer hasn't developed good judgment or self-critical skills yet. They may well need a group which has both peers and more experienced writers, who can offer a diverse spread of critique and commentary. The diversity is important to avoid the group having a single voice, as there's a definite "workshop effect" of people writing to meet their group's (often unspoken) expectations.
This means, for example, that a group composed entirely of new writers doesn't necessarily have the experience or perspective to provide varied, market-aware critique. At the same time, a group composed entirely of mid-career writers would be accustomed to addressing issues of craft and career which a new writer is probably not prepared to handle.
It's like playing chess, or tennis. You want to work with people at or just above your level. That, of course, requires an honest assessment of what your level is. Sales track record is a good rough metric, but not accurate.
You also need a group which doesn't have a overwhelmingly dominant driver. I'm not talking about the presence or absence of a sponsoring pro (the "tall pole" group I mentioned in my earlier post), I'm talking about a person or persons who overmatch the group dynamic socially. This can create an unfortunate dynamic, often unconsciously so -- for example, someone with passionately held opinions about writing, who has to express them constantly or "correct" other people.
One of the purposes of the Clarion method of workshopping is to deal with that issue. The one minute/no dissenting voices rule allows every opinion at the table to be brought forth in a conversationally protected space. Groups with open or round robin discussion, especially without orderly meeting management practices, are highly susceptible to the dominant player. Human nature, not ill intent.
Likewise, the group needs to be of a similar degree of career commitment as the individual. If you're bucketing along writing a story a week or some such madness, a group that meets monthly over tea to discuss one or two manuscripts is probably not right for you. I'm not arguing against writers having social gatherings, far from it. Just make sure your expectations and the group's behaviors are aligned.
Finally, you don't have to like the other writers in the group, but there has to be mutual respect. Critiquing is not a blood sport, nor is it for counting coup. If you find that going on, find another group. If that group doesn't work for you, find another. Check out college libraries, go to your local or regional conventions (and especially the pro workshops there), ask at the science fiction/fantasy bookstores in your area. Failing that, try Codex, Critters, OWW or one of the other online resources.