I think I am qualified to answer this question as I graduated from IIT Kharagpur Geology and Geophysics department and I am working for ARM Group in the Middle East.
You should choose IIT Kharagpur due to following reasons:-
I will highly recommend you against joining IIT Jammu as it lacks the necessary academic environment and facilities required for a rich Engineering course. My aunt is not only a graduate of IIT Kharagpur (Applied Geology) but also is currently working for Schlumberger in the Middle East.
IIT Kharagpur Geophysics is a good option only if you are interested in the field or have no other option. Honestly, the demand for Geophysics is gradually deteriorating and in the upcoming future, it will generate very less revenue and jobs in the oil industry. This definitely does not mean it lacks lucrative opportunities. Someone who is genuinely passionate about Geophysics will always choose this over other branches.
This program is not for everyone but it can be the dream branch for some.