offer from University of Bristol and Queen Mary, university of London for LLMWatch
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I chose my current university (Utrecht) because the Public International Law LLM had a sub-track in international human rights law and a couple other modules I liked. One of my friends picked Leiden's Public International Law LLM because it had international criminal law modules which Utrecht don't have. It is the same in the UK.
The difference reputation/ranking wise between the two you're looking at is marginal. Pick where you actually want to live. Make sure you visit and meet the staff, ask questions, see how receptive they are. Then once you've seen both you can follow your gut of where would be best for YOU.