Which is a better course electronics and communication engineering or electronics and computer engineering?

Both are good branch. As it totally depends on your interest. Electronics and Computer Engineering is a branch of Electronics Engineering which deals with the effects of electrons to build components, devices, systems, or equipment. Electrical Engineering basically deals with the study and application of electricity, electronics, and electromagnetism. A bachelor's program in Electronics and Computer Engineering gets you a B.Tech degree in Electronics and Computer Engineering. Computer engineering deals with the design of computers and computer systems. This may involve the design of new hardware or software. Computer engineers may also work on a system's software. However, the design of complex software systems is often the domain of software engineering, which is usually considered a separate discipline. Electronics and Computer engineering is the integration of electrical engineering and computer science to develop computer systems. The computer engineers are involved in hardware and software aspects of computing.

Electronics and communication engineering:

ECE students could also pursue in the communications, networking, and broadcast, transmission systems work area. This work is mainly targeted to consolidate electronics, conceptualize the communication network framework, and ensure its flawless execution.This branch mainly deals with analog transmission, basic electronics, solid state devices, microprocessors, digital and analog communication, analog integrated circuits, satellite communication, microwave engineering, antennae and wave progression. It also deals with the manufacturing of electronic devices, circuits, and communications equipment.