I am French and I am considering a UK LLM or a US LLM. I was thinking about Columbia in NY and King's College London in Europe. Do you know which was has the best reputation worldwide?...

I heard that King's College London was very famous in Asia?

In particular I would be interested in working in Asia or Middle East in finance (Dubai, Singapore, Hong Kong).

I won't have any doubt, Columbia Law School (as all other top four U.S. Law Schools) opens doors that the other universities don't.
If you want to find a place in Dubai, Singapore or Hong Kong having an LL.M. degree from Columbia will allow you to do so. Few friends of mine that attended Columbia last year got many offers togo to such places but since they got also offers in New York they decided to stay there.
Good luck withi your application (it won't be easy to get admitted to Columbia...trust me...)

please go to CLS... its a ridiculous comparison, im sorry, i dont mean to demean KCL, but in terms of reputaiton, very few UK schools match up to the ivy league reputations of YLS, HLS, CLS... and you should consider other US schools too... admissions are tough, but the reputation of the top 10 us schools is better than all UK schools (leaving aside Oxbridge of course. which are right on top with YLS, HLS)

OK Thank you for your answers. I just assumed that King's could compete as it is often listed as one of the best LLMs in Europe...Thank you anyway as Columbia seems to be a better choice. I'll work at it then!

Columbia is for sure a better choice

Columbia Law School without a doubt

CLS vs KCL 5-0