Both branches are a little similar and interesting. It certainly doesn't make much difference in terms of job and career if you are in a good IIT or NIT. EIE is very theory based subject. The core subjects of measurement and instruments are nearly completely theoretical but very interesting. The control part subject is mathematical as well as concept based.

Honestly, ECE is more popular branch than EIE. Most of the times ECE is the most favorable stream among the core branches. The highest placement every time is from the tech branches, and after that ECE gives highest placement in core companies and sometimes in tech companies too.

But EIE also has a growing scope in India. EIE mostly deals with the manufacturing and more detailed understanding of the functioning while ECE basically focuses more on the transmission and communication.

As you are in NIT Agartala, which is a very good college, your placement from either of the branches won't be much different. So you should decide you branch to choose on the basis of your interests.

If you choose EIE :

PRO'S

• you will learn more of the theoretical aspect of  instrument. So if you are interested in research type jobs then this would be better for you.
• An instrumentation engineer is basically needed in every industry as every industry is someway or the other instrument based. So it gives more job opportunities.
• Instrumentation engineers have almost the same exposure as EE students.
• Lesser competition in all India exams like GATE, as there are few people taking up this course and fewer colleges giving this degree.
• EIE students can sit for almost all core sector jobs, except chemical or civil  But ECE students aren't preferred in electrical and other core backgrounds and since there are few communication based core companies in India, there chances become less.
• If not anything else, EIE students can also go for software industries, which is basically open to every stream.

• CON'S
  Although as I mentioned the competition is less, the seats for higher studies in Instrumentation are also less and in some core sectors EIE seats are lesser than compared to other core fields (not always).
• The subjects are very theory based with lots of diagrams at work. So if you aren't good at elaborating things which you have understood (as is the case with me), your grades may take a hit in those subjects.

Properly take your time and decide.

Hope this helps you.