Hello aspirant ... If you really wants to become a software engineer than you have to choose cse and there is no competition issue because in cse branch you  will study about software development etc.. but in ece branch you have to study about electronic components there is a little programming involved in this couse but it's not sufficient to be a better software engineer...

1.      CSE gets you job in service based IT industry and in product based companies alone. ECE gets you the same job and additionally it provides you opportunity in core electronics and telecom industries. Also there is scope for government jobs too.

2.      CSE teaches C, C++, JAVA, DBMS and some other concepts which will definitely help you in IT sector. ECE teaches C and OOPS & DS in C++. It teaches you the basic programming.

3.      CSE has some ECE papers like digital electronics, Microprocessor and Microcontroller etc. ECE has computer papers like Computer Network, Computer Architecture etc.

4.      Computer is an electronic device. And Electronics had become more software and coding related. Both computer and electronics coexist together.

5.      If you want a job in IT sector, go for CSE. If you are not sure but in mindset to decide among variety just go for ECE.

6.      Almost every CSE and ECE graduates who got job in campus interview were all selected by Service based IT companies like TCS, CTS, Wipro, Accenture, Infosys, IBM etc.

So, choose accordingly.

Good luck!!