Nepal

Please check website of both the universities for accreditation and recognition data.

The criteria for foreign students is the GMAT exam.

Dear Suru,
Without any doubt, you should choose India because you will get the excellent study module and wide range of courses. There are many best universities which offer courses which you can't find in Nepal such as nanotechnology, microbial technology, nuclear science and stem cell technology. Even after completion of your education, you can search for good job and companies that you can't find in Nepal.
All the best.

I have mentioned below two premier institutions as desired by you. One of them is affiliated to Pokhara University where i have worked 13 years.

Officially, you have three esteemed institutions in Nepal. They are esteemed organizations because they have good infrastructure, learning materials are hi - tech (still improvising) and most importantly Government of Nepal and India has a serious eye on these institutions to enhance the most important language i.e. Sanskrit, in lieu of protecting Hinduism.
They are:
1. Mahendra Sanskrit University
2. Balmiki Vidyapeeth
3. Ved Vidyapeeth, Pashupatinath.
The chosen candidates are also taken to Pashupatinath for special bhajans.

Only, if you're a citizen of Nepal.

Students seeking to take admission under DASA also need to have a minimum eligibility criteria. They need to score 60% aggregate marks (average of all subjects of qualifying examination taken together) or 6.50 CGPA (on a 10 point scale) or equivalent in the qualifying examination. It is higly unlikely that you will be able to get admission in nsit with your score.
Check
https://www.dasanit.org/dasa2016/documents/DASA_UG_2016_brochure_16-12-2015.pdf
for more details.

I think jee main or advanced is conducted in Kathmandu . You can read Jee information bulletin for more information.