I've only had to use Groups Engine three or four times. Each time it's been easy to handle creation and management from the WordPress Dashboard.
You add your groups on the backend with all the relevant details and drop the shortcode into the page you want to populate your groups on. Though I prefer groups to be tied to my ChMS, Groups Engine is functionally the equivalent of the best ChMS solutions. It also works well with all the themes I recommend.
If groups are your thing...
If groups are your 'selling point' in church I want to suggest and unsuggest (that's not a word, but it is now) a few ChMS that I love and are group centric.
This is from my experience working with each of these. If they've made updates that make group management easier, I'd love for you to drop me a line and tell me about it!