Also the duration of passport issued by embassies is of shorter duration if I am not wrong.
I read and it says that after renewal they send back the old passport and the visa on old passport remains valid till it is expired.
True, if you continue to stay there. But what if you step out of US, back to India, say for vacation. Even I am not sure, but just double check for info if needed
I guess not needed
http://www.ustraveldocs.com/in/in-gen-faq.asp#8
Q.8 My passport has expired, but the U.S. visa in it is still valid. Do I need to apply for a new visa?
No. If your visa is valid and unmarked or undamaged, you can travel with your two passports together (old and new), if the purpose of your travel matches your current nonimmigrant visa. Also, the name and other personal data must be the same in both passports (unless the name change was due to marriage), and both passports must be from the same country and of the same type (i.e., both tourist passports and both diplomatic passports).
If your name changed due to marriage, you can travel to the United States with both passports as well as your marriage certificate.