This is useful infotmation to learn, but I can tell you from having done all three that consulting for a shop is as different from freelancing as it is from an in-house job.
I guess it depends on how close you are to the sales process. I have had a chance to get a lot of experience working on proposals from a tech point of view and am involved in the pitch and negotiation. There is definitely carryover from those activities. But if you are consulting as a heads down IC and leave other aspects of projects and bids to the “business people” I can see where you may not learn as much that will be helpful as a freelancer.