Which MBA college should I prefer (background is from B.tech hons (CS) and have 15 months work experience), IIT KGP or IIM Trichy?

The best way to answer your query is to mention the core highlights of MBA from both institutes.

IIT

• The MBA course here is more of technical nature as the program is one of the many departments of a huge Technical institute
• The peers are very talented and genius 
• The small batch size increases the opportunities for placements 

IIM Trichy

• The MBA experience here is much more diverse and challenging. You will find peers from diverse backgrounds.
• The pedagogy here is top notch as they specialize in this area
• IIM Trichy has a better academic rigor and their style of Management education is too good
• IIMs offer better food and infrastructural facilities 

I will sum up my answer with 2 points. If you are looking for job prospects outside India, IITs are a good choice. But within India, IIMs are a better option as their style of Management surpasses that of IITs.