I have got admission offer for LLM Course from LSE London (UK) and Coulmbia Newyork (USA). Which institution will be better in terms of employment opportunity at UK and / or USA or other countries. I am from India and already done LLM from a premier institute in India. I am aged 26 years.

I'm from London and I would say 100% go Columbia. Masters degrees from USA are harder to get into than they are in the UK and employers know that. Having said that if there's significant cost difference in fees, London is a fabulous place to be.