Hi there Steve,
I'm pretty familiar with Ning, but I hadn't heard of Elgg or Dolphin before today. So I can't really give a very helpful answer. Hopefully we can find some other people to speak specifically to those services.
One question I had, though, is about the extent to which you want to be able to moderate activity. For example, on a site like Ning, you can certainly moderate blog posts and comments, but I don't think you can monitor private messages that members send to each other. For that, I'm pretty sure you'd need a self-hosted service.
Perhaps if you're able to explicate both what kind of activity you'd like to see happen on the site and what kind of control you'd like to have, the right solution will make itself more apparent.
Happy Friday,
Elliot