Which branch should I take in NIT Silchar mechanical or ECE?

In my opinion, you alone can decide the best branch for yourself and others can only guide you. If you are evaluating and comparing branches based on placements, then trust me it won’t help in the long run. Unless you are genuinely interested in the branch, you won’t be able to pursue a career in it for a long time. 

Mechanical 

• If you are inclined towards stuff like automobiles, heavy machinery, or design, or want to work in a good PSU then choose Mechanical.
• One needs to be aware of the fact that this branch is completely core-based so you will be studying only core concepts for 4 years. 
• The placements of core mechanical are quite better than ECE.
• Students of the Mechanical branch can go for Mechanical-related jobs only and most software companies won't allow Mechanical students to sit for their placements. 
• Mechanical has more PSU placements but Mechanical has much higher and tougher competition compared to ECE.

ECE 

• If you are interested in small electronic devices, Arduino, IoT, Integrated circuits and diodes, fabrications, and chip design, or want to pursue a career in coding and programming then you should go for ECE.
• This branch is a mix of core ECE and software/IT, i.e. ECE's major role will be played by software only during placements.
• ECE core can be helpful if you want to pursue higher education.

So, make sure you go for the branch that intrigues you and not the one that offers better placements.