I'll give you a concrete answer. I don't want to give a vague answer with sugar coating or wired fan boy answer. After you have read my answer , you will end up with a much better perspective.
1. Go for MTech only if you wish to get into teaching or Research (PhD)
Unless you do your MTech from IIT or IISC, chances are, the only door an MTech will open for you is Teaching or Research. Most folks feel that an MTech in Mech will increase their chances at good profiles in core companies. Lies, when it comes to Mechanical Engineering, experience beats advanced degree 9/10 times.
2. MS (Only if it's USA or Germany )
Unlike India, USA and Germany have a strong manufacturing Industry, India has been fashioning itself into more of a Software/IT hub.
So, going for your master's in US or Alemagne, will probably help you more to get into a specialised industry role than an MTech will do so here.
3. Work at a core company
The respect you will get from your batch mates and teachers will be immense if you get into a core company in a core profile. Reason being simple, most Mech folks end up in IT. You being in you branch will garner immense respect , not only from the above-mentioned people but also other potential recruiters. Shift from one core company to another is much easier than from IT to Core (not impossible).
4. Work in an IT/Analytics/Non-core company
We all need to work for a living, there is nothing wrong with that. If you do not get a job in a core company, it's stupidity to rejecte all other jobs waiting for that one ideal job.
5. Go for an MBA
I know many mech engineers who were very ordinary at their Mech subjects or jobs but ended up being rockstars of economics, Investment Banking, marketing and business development.
6. Civil Services/UPSC
One of the greatest Engineers of India, was also one of its best administrators, Sir M Visvesvaraya. Other famous administrators are Jairam Ramesh, Manohar Parrikar etc.
Do I need to say anything?.
Remember, grass isn't greener on the other side, it's greener where you choose to water it.