The quality of the department has much more influence on the degree than the "famousness" of the campus—whether it is a "main" campus or a "branch" campus.
For instance, in my field, Chemical Engineering, the University of California has two departments that are widely acknowledged to be top ten: Berkeley and Santa Barbara. A degree from either of these schools would be recognized as essentially equal; degrees from campuses like Davis or Los Angeles would be slightly less well received, but still be considered good.
So, to some extent, it's more the issue of the resources available at a given department, and its reputation within the community as a whole, that makes the difference. The campus as a whole is a distant second. (As a similar example, the University of Minnesota is recognized as a top-five program in my field; nobody would rank UMN as top five nationwide overall.)