Which should I choose: Electronics and Instrumentation in BITS Pilani Goa Campus, or Electrical and Electronics in NIT Surathkal?

Since both the colleges are considered highly reputable and among the best in the country, you should focus on the branch. The choice of the branch directly depends on your inclinations and future goals. 

To make it easier for you I have explained each branch in short:

Electrical and Instrumentation: 

• Instrumentation engineering is the engineering specialization that focuses primarily on the principle and operation of measuring instruments that are used in the design and configuration of automated systems in electrical, pneumatic domains, etc. 
• These engineers usually work at chemical or manufacturing plants and their job role involves improving productivity, reliability, safety, optimization, and stability. 
• They are responsible for designing devices that measure physical quantities such as pressure, flow, and temperature. You will require a lot of knowledge in physics much more than electromagnetic theory. 

Electrical and Electronics:

• In this students learn to design electronic circuits, and computer systems and also develop control systems. Electronics play a key role in the implementation and control of electrical machines. 
• The course mainly focuses on designing and testing ICs, inductors, capacitors and resistors and includes fundamentals and principles of physics, mathematics, computer science, and project management. 
• The sub-disciplines of this branch are power, control, electronics, microelectronics and Signal Processing, Telecommunications, Instrumentation and Computers.

Although the choice depends on your own interests, EE has a better scope than EIE.