I've just finished an LLM in Public International Law at Utrecht University and will be going into academia as a PhD student and graduate teaching assistant back home in the UK.
Depends on the specific subfield of law but when talking about law schools in the Netherlands it is always Leiden this and Leiden that with Utrecht and Amsterdam a close second and third. It is because Leiden and Utrecht are the two of the oldest and most established with excellent alumni.
I wanted to reply to you because you said you do better in coursework. The Netherlands have many many exams on their LLMs. They still operate on the system that you probably had on your LLB that there has to be some balance between assignments and exams like 50:50 or 40:60 at least. LLMs in the UK generally aren't like that are assessed by all essays. The academic calendar here works that you get two modules per block and there are 4 blocks. You'll have 3 8 week blocks of teaching and then the last block will be the thesis. This means the assignments can be quick fire and the modules sometimes not the level of depth I expected. Also the actually grading is wildly different at different universities here. Leiden and Maastricht grade notoriously low (I've heard horror stories of like half a class failing a module at Leiden on one of their LLMs) whereas Utrecht have a higher grade curve in the law school. Not sure about Amsterdam. I'm not ashamed to say that getting *** laude (UK distinction) is easier at Utrecht. I'm afraid I don't know what the marking is like at Rotterdam or Groningen.
That being said there are bonuses. I've had opportunities here that I wouldn't have had if I did my LLM in the UK. I've covered more ground because of the number of modules and been able to pick and choose more. We had some varied assignments too like mooting modules where we did written and oral pleadings. I did a mooting competition in humanitarian law which is my favourite. I serve as an editor of a peer reviewed journal at Utrecht and Utrecht paid for me to go to Croatia on a course related to my future PhD project. These are all things that we don't really have access to in the UK, or at least less access to.
Regardless of formal rankings it is reputation that matters more. Leiden, Utrecht, Amsterdam (UvA), and Maastricht degrees are largely regarded to be as good as at least Russell Group in the UK with Leiden and Utrecht roughly the same as a UK top ten uni. My Utrecht LLM managed to land me a funded PhD place so I can't complain and it must have been well regarded. I would say Groningen has a better international reputation than Erasmus from what I've heard. Groningen have a really good EU department.
I would discourage you from staying at Bristol for your LLM. Going elsewhere will massively improve your network for academia and shove you out of your comfort zone which is good for improving skills. From what I've seen on the CVs of people who stayed for LLMs where they did their LLBs they kind of exhausted all the extracurricular opportunities early on and then had a little less on their CV than someone who went elsewhere and got thrown into new things.