Engineer scope

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

It has a very good scope. Teaching is very average here at RV college of engineering. Placement opportunities are really good here. Average salary is around Rs.5 lpa.

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

The scopes keep varying from time to time Ajay. Both branches are good.

Aircraft Maintenance Engineering course will prepare you to have role of service engineer with airlines by training you on all aspects of aircraft operation and maintenance including handling & servicing of ground handling equipments. In order to get a job you will have to obtain a particular aircraft maintenance license. As it is a niche profession, jobs are lesser but jobs are very high paying.

Of course, there are opportunities with various Airline companies, Airport Authorities etc. as Service Engineers

You can't decide either way. With hard work, a Lawyer gets a lot of money, name and position in the Society. An engineer gets employment, without much struggle, normally. You decide, according to your inclination and aptitude.