B.Tech

ECE and EEE are the branches which sound quite similar.
EEE actually goes deeper than just "motors & generators". You also learn more about electromagnetics and how high-frequency signals operate - this is the black-magic that's required to design computer and wireless Systems, one can make more money as an EEE.
ECE: Here, it deals with electronics with some part of communication. The subject uses the scientific knowledge of the behavior and effects of electrons to develop devices, systems, or equipment that uses electricity as part of its driving force. Also, it contains basics on electrical machines and more on integrated circuits and communication systems. As far as scope is concerned, both EEE and ECE are evergreen branches. ECE students can get into IT sectors easily, while the demand of EEE students is high in core companies.
Personally, I feel that the stream might be unique but the only thing a student should focus on is the future goal. Once, he is sure with that, he can then choose the stream of his choice. So, I suggest ECE branch rather than EEE and it also depends upon your choice whether to choose ECE branch and shift to either (software, core) or else go deeper with the subject and choose EEE branch and target a job in the core companies.

The differences-
The CS engineering programme usually deals with how to build microprocessors, how to write a compiler, etc. IT is the business side of computers - usually dealing with databases, business, and accounting. One way to think of it is that IT deals with the application of computing technology to real life processes and CSE deals with the Science that facilitates these applications. Further, while CSE focuses on the foundation of computing, IT as a discipline focuses on satisfying the computing technology needs of organisations. So, in a continuum between principles and application, IT focuses more on application, with the goal being to apply knowledge of computing sciences for solving problems. However, as the foundations of IT are in computer science, Indian universities and colleges deem it feasible to have a CS-based IT programme.
This allows a graduate of the programme to choose a career in CS or IT, based on their choice and availability of job prospects. And mostly corporates make little difference between these disciplines while selecting students. The nature of the industry requirements in the country also plays a crucial role. Since most of the companies in this sector focus on application development and maintenance at best, the need for hard core research level employees is minimal. So even if a student is taught subjects like chip design architecture, machine level languages, his or her chances of getting a career in that domain is minimal.
The verdict:
If you have to choose between IT and CSE and have both options in hand, it would be wise to decide it on the basis of the reputation and standing of the college rather than the branch. If you have to choose between IT and CSE in the same college, see what excites you more, design of computers and computing systems or using computers to solve information management requirements of organisations.