Aircraft Maintenance Engineer

It is easy to pick up mechanical engineering for Avionics engineers, vice versa may not be true. With sophistication & development in avionics - I prefer avionics.

AME is a niche branch of engineering in whichever you are only eligible for aircraft servicing and maintenance jobs. You will get very little aircraft design exposure. Scope is limited to a smaller industry. Aeronautical engineering has wider scope. Therefore, it will better if you do aeronautical engineering in place of AME.

College should be good, whether it's a private or a government college. For further details check out the link :
http://www.highereducationinindia.com/career-options/careers-in-aircraft-maintenance-194.php

Click link below :
http://www.payscale.com/research/IN/Job=Aircraft_Maintenance_Engineer_(AME)/Salary

Follow link :
http://www.indiastudychannel.com/resources/143707-scope-Aircraft-Maintenance-Engineers-India.aspx
Avionics will be a better branch to opt

Check out the article :
https://www.shiksha.com/become-an-aircraft-mechanic-article-4586-1

Check link and filter colleges according to location :
https://engineering.shiksha.com/aircraft-maintenance-engineering-colleges-in-bangalore-categorypage-2-61-1-0-0-278-106-2-0-none-1-0

Eligibility criteria to be an aircraft maintenance engineer, is +2 with physics, chemistry and mathematics. You are not eligible for AME.

You should choose aircraft maintenance engineering.