In terms of placements, Computer Science takes the lead, hands down. Average package at CSE is Rs. 6,00,000, whereas for ECE it is around 4,50,000. (Not including mass placements)
CSE leads to Software engineer/Software Analyst/Technical Analyst roles.
ECE either leads to core placements like Hardware engineer/Technical Consultant or Business Analyst roles.
Although, you should make your decision based on what you think you are likely to enjoy. If you enjoy programming, mathematics or logic, go for CSE. If you enjoy Hardware design, Physics, Mathematics and simulation based programming go for ECE. Both are, IMO, the best branches at VIT (Vellore) and will bring to you an abundance of engineering opportunities and exposure. How you tap into these opportunities though, depends on you.
Also, whoever told you the CSE is a dying/slowing down field, is an uninformed idiot (No offence).
Look up areas like Machine Learning, Data Mining, Computer systems, Security, Graph Theory, Algorithm Design etc. No other branch, in my opinion, affects you in your daily life, as much as computer science.