the Intrepid Tour
I found out about Intrepid through their association with Oxfam — they used to run Oxfam Journeys — and their responsible travel emphasis.
This tour was my first experience with a commercial organised tour, as the group trips I'd been on before had been organised by universities or NGOs. It worked out well: the organisation was solid, with hardly any hiccups, and there was room for us to do our own thing in many places.
Perhaps the most important factor was the people. Chinzo was a fantastic local guide, Patti managed to lead the trip in such a way that she felt more like one of the group than a leader, and our fellow travellers were a great bunch of people. They had interesting stories to tell during the long road trips and useful skills — notably a doctor and a birdwatcher. (One drawback here is that one ends up talking to one's fellow travellers instead of the English-speaking locals, let alone making the effort to learn some Mongolian.)
Of course there's always a chance factor in the people one ends up travelling with, but based on my experience on this trip I'd certainly do another tour with Intrepid.
The local operator who managed the tour logistics for Intrepid was Happy Camel.