Automobile engineering is a sub branch of mechanical engineering, though it is studied as main branch in some engineering colleges.

Difference according to study

In mechamical engineering you will learn every mechanical object or machines out there in the world. You will have more generalised subjects like theory of machines, dynamics and kinetics of machines. You will have machine oriented problems.

While in Automobile engineering you will learn Automobile IC engines, Vehicle Dynamics, Vehicle kinematics, etc

Difference according to career opportunities

You can get your job more easily with degree of Mechanical engineer than Automobile engineer. Truth being that every firm prefers mechanical Er. over Automobile Er. Even some automobile companies prefer Mech. Er.

If you are looking for masters in Automobile engineering than this can be good option.

Automobile engineering is subset of mechanical engineering. It includes all design studies and innovation related to automobiles

Whereas mechanical engineering includes all solid, fluid and gas mechanics.