What if one pursues a PhD from a university campus which is not the main campus, rather in a different city hundred miles away. The certificate is given by the main campus authority. Is there any discrimination towards the graduates?
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.)
Often a university will have many campuses, and some campuses will be much more prestigious than others. (One well-known example is the University of California, Berkeley, versus UC Merced.) In that case your degree will generally be more highly regarded if you go to the more prestigious campus.
However, I think the example you mentioned does not fall into this case. (After reading the link you sent, I couldn't quite decide, but I got more information from the wikipedia page for UNSW.) So in your case, I would ask about which resources, particularly classes and faculty members, you will have access to. Elsewhere I've written about why you should go to the best grad school you can get into. One big reason is networking and another is the culture and mindset you will absorb from your classmates and faculty. Even if you have the same degree on paper, many people will know (or think they do) if there's a difference in the quality of your training.