Hello aspirant,
Both the institutes are very good with great placements. But in my opinion you must go for cse in nit Trichy as this is the best NIT in India and is ahead of many IITs as well. The NIRF ranking of NIT Trichy is 9 and that of DTU is 36.
Average CTC of DTU is 10 lpa with 80% placement whereas that of NIT Trichy is 14 to 16 lakhs and highest being 42 lakhs with more than 90% placements every year.
But choose according to your needs, where you will be comfortable according to your native place. But, I would recommend explore the world, don't restrict yourself to your native place.
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