ilostmymarbles, reputation is important, true, but you overestimate vastly the difference in reputations between the two schools in question. The THES, (The Times Higher Education Suppliment) placed Cardiff in the top 100 Universities in the world this past November. The Research Assessment Exercise is set to refute your league table, which if you read the methodology is not actually as pertinent to graduate education given the weighting that it uses. The fact is, rankings are everywhere, from the Guardian, to the Times, to U.S. News and World Report, to Petersen's to Princeton Review, and guess what, they are all different. So who is right, well probably no one comprehensively but given most of them have these two schools very close together (in relative terms) and the UK government's rating system for the field of research in question is likely to yield a far different result for postgraduate politics than you assume it will, I suggest that those reading this, particularly the original poster, make up their own mind based on the emerging data and bear in mind the potential subjectivity of your source. I'll ignore the combative nature of your post and simply say that it is easy to dismiss someone on the internet, which you are welcome but ill-advised to do, and I simply hope that the people who read this thread and most importantly the original poster who asked for the advice, see the subjectivity of your opinion. We are not talking about the difference between Harvard and Southern Tennessee State here, we are talking about the difference in reputation, if any (which I would debate ardently) between Princeton and Harvard or Smith and Wellesley or JHU and Stanford.
Employers may care about reputation, but remember what you are talking about here, this is POSTGRADUATE level education in politics. Unlike undergraduate CV name recognition, it matters much more in this field what the specific program is, what it covers and the individual intellectuals that comprise the department itself who you would directly study with (and in turn get recommendations from). So depending on what these people specialize in, and the field you wish to enter, the reputation of the schools, if comparable, is not of primary importance when one is specializing (as postgraduate work is) in a very specific subfield. Cardiff and Edinburgh both have their strengths within their respective departments and this is why the decision really comes down to that. Specific strength in a specific program.
For example, let's take meteorology. One might think that the best place to go for this is say MIT (tier 1 USNWR) where technology and science are paramount and it is arguable one of the top ten schools in the world. However, one of the most highly regarded meteorology programs in the world is at Lyndon State College in Vermont, a tiny tier three (U.S. News & WR) school. Within this particular field, the two schools have very good reputations but are very different so depending on what your particular interests were, say becoming a TV weatherman or alternatively becoming a dopplar radar engineer, you might make very different choices as to which best met your needs. Furthermore, this choice would not likely, or perhaps I should say, ought not likely come solely based upon the tier or reputation each possesses as a whole but where the school stands in the field.
To say Cardiff does not have strengths in politics that Edinburgh does not have is patently false as is born out by any articulate examination of the department. Likewise to say Edinburgh does not have strengths in politics that Cardiff does not have would also be false. So when specializing in some aspect of politics, especially as a masters or Ph.D. student, it is paramount to go to decide between these two very good schools based upon which best prepares and stewards you for the field you wish to research. This answer will not always be A nor will it always be B.
As for students you know. This is actually helpful, however perhaps even more subjective than the previous assertion. I can say that I have really enjoyed my time at Cardiff and my postgraduate experience. I also suspect that most colleges and universities are disorganized administratively, although some more than others. So not to contradict you, I'm sure these students have legitimate reasons for feeling that way, it has not been my experience here.