I would definitely go to Bristol, particularly if you want to work in academia. Academia is incredibly competitive these days and going to Bristol will (rightly or wrongly) improve your options for your PhD.
I'm assuming that you already have ideas about your doctorate and research area so look at this too and factor that in to your choice.

I wouldn’t necessarily say it would compensate but, as you will see, once you get to PhD level, where you did your undergrad is of less importance than your research proposal. There are quite a few academics who have degrees from post-92 universities.

The thing that will make or break you is having an excellent research proposal for your PhD and securing funding for it. Is your masters degree a taught one? Doing a research masters will stand you in better stead to be honest but I presume that you will at least have to do a dissertation.

If you want to be an academic, start looking and applying for funding opportunities ASAP. Identity who you want to supervise your research and ask for assistance with funding applications.

Academia is pretty tough and very competitive so make sure you go into it with your eyes open.

Oh and I don’t know why the knocking of Cardiff. It’s also a RG university and has an excellent reputation and I wouldn’t say there’s a big difference in prestige between the two institutions, although Bristol is currently higher in many largely meaningless league tables.
It sounds like the course at Bristol is better, which would make me pick that but choosing postgraduate courses on the basis of perceived prestige in undergraduate league tables isn’t a great idea. If you live close to Cardiff, this might mean that this would help you integrate more into the department whereas being far away from Bristol could make you more isolated. However, as the course isn’t as focused on what you want to do, it would make sense to pick Bristol.

What's an LLM?

Master of Law I believe. A postgraduate law degree.

Is it possible to go straight to PhD with the masters year attached so basically the first year being research methodology etc and then you build on this for your doctoral thesis?

In many ways the advice that an LLM isn't useful is correct. If it's research based then it has worth in terms of learning how to do this correctly and effectively but otherwise it would be better to go straight to a PhD with a foundation year. An LLM is a good way for law schools to make money.

Does either institution have a 1+3 PhD programme or a more research oriented masters? LLMs are massive cash cows for universities and the students often receive little training for the PhD as a result.

Have you contacted your potential PhD supervisor? I would not say there is a lot of difference between the two schools, both are good ‘regionals’ and good quality academics are at both. Keith Stanton is a well respected figure in public law who has been at both Bristol and Cardiff.

Sorry, I meant Keith Syrett.

www.bristol.ac.uk/study/postgraduate/2020/ssl/msc-socio-legal-studies/

How about something like this OP? If you could get 3+1 funding that would put you in a good position for a future academic career.

Also when you say less than desirable undergrad do you mean the university rather than the result? Because to get any sort of PhD funding I think a minimum high 2.1 is needed and a masters won’t make up for that, no matter where it’s from.

I’m director of PhD admissions at my law school (RG London) and my counsel would be to get your info from the schools you wish to apply to. If you can identify a potential doctoral supervisor(s) and work with them to develop your proposal (and structure your LLM to best prepare you for that) then you would at the very least be giving yourself the best possible start. The grades of course are your responsibility. That said, for all doctoral applicants, provide they meet the entry criteria - and I would say that in law, it is unusual to discount the LLM result and/or go directly into the PhD with only an LLB - much would depend on the quality of the proposal and the supervisory fit. Admissions requirements are a filter to some extent but they are not a block to those who can demonstrate their suitability in other ways.

I would also not listen to your institution’s careers office unless they have experience of advising would-be academics rather than people who wish to increase their training contract chances by compensating for a less than stellar undergraduate result with an LLM from a higher ranked institution.

Good luck!

Having had a little pootle around the Internet, I wonder if you would consider an online or distance learning LLM. The public law offerings at both Cardiff and Bristol look quite limited to me (I am a public law academic). The LSE has an excellent looking public law specialisation on its ‘executive LLM’ and of course there is also the University of London’s long-standing and well-respected international LLM programme (UK students are eligible) with lots of public law options. At the schools of the UoL, IALS offers an LLM in law making and legislative drafting and there is also the MA in human rights offered by the SAS.

Good luck!

If you know you want to work in academia, you need to think about where you want to do your PhD rather than just your LLM. That means looking into funding opportunities at different places.
I can’t see your application to be admitted to a PhD hinging on whether you did your LLM at Bristol or Cardiff but would you be up for commuting to Bristol for a further 4 years for your PhD or would it make more sense to be closer to home?

I agree with the pp who said to take advice from the universities themselves rather than the careers department. Careers departments aren’t that clued up about careers in academia. Getting accepted for a PhD won’t be the hard part, getting funding will. That’s why it’s important to start doing the groundwork before you even start your masters and begin chatting to potential supervisors.