Which branch will get government job easily - Civil or Mechanical?

The 'branch' does not make it easy or difficult to get a job. Hiring, at government or private companies is mostly driven by two things: skills and experience. 

Of course, branch would come into picture if you have figured out what kind of government job you wish to get in. However, you have not specified it. 

If you like working in the civil domain - go with Civil engineering, else pick up Mechanical engineering. The key here is to acquire relevant job skills which will make it easier for you to get the job. 

India is building several mega projects, so infrastructure development is definitely a booming sector right now. Civil and Mechanical engineers are already seeing a change in the number of vacancies in government jobs, thanks to Metro development, railroads connectivity, and smart cities.

It all comes down to what you would like to do. If you choose a branch just for the sake of 'better job opportunities', you will be in trouble my friend, some 7-8 years from now as you would start hating it if it's not the job that interests you. You will find any job exciting if you enjoy the underlying subject matter.

I'd suggest that you carefully choose a branch after going through the entire 4 year syllabus of each and see what appeals you.

 I think it depends on the capability of the candidates, government jobs are likely to get for every person.

Of course, the branch would come into the picture if you have figured out what kind of government job you wish to get in. However, you have not specified it. 

If you like working in the civil domain - go with Civil engineering, else pick up Mechanical engineering. The key here is to acquire relevant job skills which will make it easier for you to get the job.