Well it's not really a generalization given that the one most competitive chambers in the UK (according to my friends on LLM at LSE) has 5 pupils and 1 is a SOAS graduate. SOAS has a niche--highly respected academically and loads of courses on human rights, which would go nicely with any kind of legal defense for marginalized people. Bristol may be a good law school but having a lot of lawyer friends and relatives in London, I don't think it has a better reputation than SOAS.
SOAS is a brilliant university and doesn't get the credit it deserves on TSR to be honest. It's one school that consistently, professionals and academics in law, politics, linguistics, etc. consider to be one of the best in the UK and on an internationally-prestigious level as well.