It depends on a lot of factors, although there are exceptions to every rule.
If you are talking about a management company vs. no management company at the same golf course, it sometimes can make a significant difference. If the course was poorly run, management companies may not always run them perfectly, but they'll usually run them reasonably well. Also, that kind of change may be accompanied by some investment or large changes in operation that can make a big difference.
If you are talking about one management company vs. another under a management contract, the differences will be smaller. The overall level of expenses is usually determined by the owner and the revenue, so there's a fairly thin margin as to what can be done within those constraints. Most management companies do a reasonably good job, so there isn't as much opportunity to improve.
If you're talking about management companies buying a course, that's a little bit different, and there can be much wider swings because now you're talking about ownership, which can have a big impact when it comes to investment, strategy, and goals. And those can vary from one course to the next, so that's not always an easy answer, either.