The scope of EEE is huge.
Electrical & Electronics engineers can work in wide range of fields such as power generation, electronics, computers & control systems, telecommunication and Bio-Medical. Job responsibilities may include specification, design, development, and implementation of products or systems, as well as research to create new ideas. This role provides a number of challenges ranging from problem identification and the selection of appropriate technical solutions, materials, test equipment, and procedures, to the manufacture and production of safe, economical, high-performance products and services.

Of course, option of further research in this field is also open.

Electronics Instrumentation engineering is a specialised branch of electrical and electronic engineering and it deals with measurement, control and automation of processes.Apart from covering core subjects such as  industrial instrumentation and process control, bio-medical instrumentation and robotics, the students deal with software and hardware topics such as microprocessor and micro controller based instrumentation, VLSI and embedded system designs, computer architecture and organisation and computer control of processes. Computer languages such as ‘C' and C++ are also part of the curriculum. This makes an instrumentation engineer fit for both the hardware and the software industry.

Based on the details and scope of both you can choose the best for you.

Good Luck.