I agree with some of the other experts here that there are regional differences. I think the difference is smaller in reality than it may seem - McKinsey does also have staffers that help match consultants to projects, to ensure efficient and seamless staffing, which can be particularly helpful when you have just started at the firm and don't know too many people yet. I believe that at Bain you still have some input over the projects you are staffed on, certainly so if you cultivate a network.
I second the experts here who are saying that networking is a crucial part of the job - you will have to network a lot to get staffed on projects you enjoy and to get promoted, so unfortunately I don't think there is a firm where networking doesn't play much of a role.
If you didn't perform well on a project, you will be given feedback about it and may have a conversation with your staffer/personal development manager if there are serious issues. You will then be staffed on other projects where you will have a chance to turn things around. Hope this helps!