I don't know which institute are you from. If you are from 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 ECE) is mathematical cum concept based.
Career wise, though ECE being far more popular than EIE, I believe EIE has more career scope in India than ECE.