Hey,

I don't know which institute are you going t join. If you are going to join any IITs or NITs, it doesn't make any difference in terms of job career.
EIE is, you are right, very theory-based subject, the core subjects of measurements and instruments are 95 % theory but are very interesting. The control part (which is common with EEE) is mathematical cum concept based.
Career-wise, though EEE being far more popular than EIE, I believe EIE has more career scope in India than EEE.
Reasons:
1. An instrumentation engineer is basically needed in every industry as every industry is somehow or the other instrument based. Instrumentation engineers have almost the same exposure as EE students.
2. Lesser competition in all India exams like GATE, as there are few people taking up this course and fewer colleges giving this degree.
3. EIE students can sit for almost all core sector jobs, except chemical or civil (Ex: NHAI). But ECE students aren't preferred in electrical and other core backgrounds and since there are few communication-based core companies in India (except biggies like BSNL, Airtel, etc.), their chances become less.
4. If not anything else, EIE students can also go for software industries, which is basically open to every stream.

Drawbacks:
1. 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).
2. 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.

Hey!

Although EIE branch is good but it is not widely spread as not all the colleges offer this branch. Only 30% of the engineering colleges offer it. While 80% of the colleges offer EEE branch as its scope is wide  . So , the scopewise EEE id better. But since maby graduates possess this branch , while lesser students possess EIE branch , so there is less competition in EIE branch. Also , the syllabus of EIE is much easier than EEE. So  , now it all depends upon you , which branch you want to choose.

Hope it helps!