Potentially, an LLB from India in combination with an LLM from Harvard, Yale, Columbia will get you to the same place, employment wise. But, three years of legal education in one of the most sophisticated legal systems with the most powerful supreme court in the world will reshape you as an individual.
First Person Accounts: Shaurya Upadhyay on the LL.M. at LSE
The reasons for you to do the LL.M will always be unique to you, so you must always look at this bigger picture, and use external advice (including this interview) only to fill informational voids.
First Person Accounts: Manasi Chatpalliwar on the NUS LLM, writing a good Statement of Purpose & more
Manasi Chatpalliwar on the LLM from National University of Singapore (NUS), working before a master's, Indian law firms and the LLM, and a whole lot more.