You won’t face any kind of dominance or bias studying at either college. The students are friendly and unless you provoke the other party, no one’s going to interfere in your business or harass you. It’s good to make friends belonging to diverse cultures rather than limiting yourself to certain cultural boundaries. Usually, IITs and NITs have very friendly seniors and peers and there isn’t ragging in any form.
Remember you are not here just to score a high grade or win medals. Rather, you are here to change your life and yourself and only learning from others' experiences will help you go a long way. So don’t worry and go for either NIT Trichy or NIT Warangal and make the most out of the available resources. Be empathetic and always think from a broader perspective. Only then can you attain new heights.