Which would be a better choice, instrumentation in BITS Goa campus or instrumentation at NIT Trichy?

There is nothing called instrumentation engineering. The students usually study the syllabus of the electronic branch that includes learning low-level languages along with the complete command of them. 

• There is a very high demand for highly skilled engineers who know the top programming languages like TopCoder, GitHub, and many more. 
• Learning these languages totally depends upon the person that they can do without going to college.
• Becoming an electronics engineer totally depends upon the person, and their effort, not the college. 
• Some of the students follow the GATE syllabus to enter into the government sectors. 
• Some get recruitment in top private companies by learning these programming languages. The college can help you out only by giving a proper study environment that can promote your overall development. 

If you wish to join the private sector, then only the placement facility provided by the college is useful to you.

Last but not least we can say that the college for the instrumentation branch is the version of the electronics branch of engineering. It totally depends on you how much effort you are putting into the same and not depend on the college.