Both have some very modern buildings and some very historic, Harry-Potterish buildings. For law, while the Wills Memorial Building (Bristol's Law school) is stunning and iconic, I'd prefer Durham's purpose-built school for practical reasons.
I believe it's silly to say, for law at least, that any of Durham, UCL, KCL, Bristol, Warwick and Nottingham is better than the other. Someone gunning for a TC will most certainly not find an employer saying "Well, he goes to Durham, so I'll pick him over the fella going to Nottingham". Oxbridge and LSE may have an edge, and to a lesser extent UCL (always in my opinion), but other than that it's very pointless to say that one is fifth and the other is sixth and so on.
Some people think the entry requirements provide a fair comparison, but I oppose that. You can't possibly compare them objectively. Bristol has a class of about 370, while Durham has a class of 270 and Nottingham even less at 170 (numbers are approximate). Obviously Bristol would be (a lot) more competitive if it had 170 places and Nottingham less competitive if it had 370 places, and so on for every school.
-That's for law but I believe it applies to most other courses as well.-
Overall, I'd advise anyone aiming at these universities to be careful on what they base their decisions on. For me, Durham was never an option in reality due to its location. I would never be able to survive in such a small city! Bristol is an amazing city and that made me choose it as my insurance (I did for a moment regret not opting for KCL as my insurance due to London, but I am very happy with Bristol now!). Other factors would include prices, opportunities in terms of careers and similar factors. Posted from TSR Mobile