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Both mechanical and automobile engineering are good to pursue as career.
Mechanical engineering is the father branch of automobile engineering.
Mechanical deals with the basics and core concepts that are used in almost every mechanical object but automobile deals with only subjects or courses that would help in making or studying an automobile altogether. Basics are same such as thermodynamics, strength of material, theory of machines, heat transfer, refrigeration etc
The better would be to do mechanical engineering as it would help you getting good job opportunities including jobs in automobile sector too.
These are some of the best universities best for pursuing your engineering:
IITs
UPES,
BITS Pilani