I recommend gaining some experience before an LLM degree. It also gives you clarity about your interest areas which helps you to design your LLM program accordingly.
Nayanthika Ramakrishnan is a graduate of the National Law University, Jodhpur ('12) and currently enrolled as a JD student ('20) at Cornell Law School.
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.
Ankit Sharma is an Indian law graduate who is currently pursuing an LL.M. from Cornell Law School