From my perspective: The professionally guided group is just that, professionally guided. Which means that there will be a huge margin of safety, and no real chances are going to be taken. With such a group, the pro often has people along that he/she has never met. In my experience, people show up with no knowledge, no fitness, no gear, no idea of the route, the dangers, the mitigation. You have to be prepared for it all. They don't have a sleeping bag, they use the guides sleeping bag. (the guide goes through the packs down below)
Private groups may comprise the same people. They may not have the same goals or destinations. They certainly don't have the "hand of experience" that the other group is paying for. They are much more "throwing the dice." (people don't look through other people's packs, as a rule)
