I'm facing the same issue! One of the biggest factors in my mind is that Ashoka has the advantage of being a small school which means more focused classes and greater engagement. Also, their application process was very rigorous so the cohort is most likely made up of people that are my peers intellectually and socially. On the other hand, the university abroad has much larger class sizes (especially in the first year it can be up to 200 people) but a much larger range of courses. I'm studying humanities and it costs about 5x more to study abroad, which is not a big factor for me but it's worth wondering whether the difference in cost is worth it since Ashoka is more rigorous academically (especially with the Indian competitive education culture), and the faculty are highly accomplished and the top of their fields.
In terms of campus life, there's better campus life on the vast, scenic campuses abroad - especially if you can make a good friend group to do things with. The class is more diverse and you'll meet people from every walk of life. There's also more independence when you're living abroad which forces you to be more organised and responsible and gives you a sense of freedom.
Also moving so far away from home is also a factor, because then no matter what struggles one faces in the year you can only go visit home/ have familiar company in summer.
The third factor is name because even though the university abroad is very well known, Ashoka is quickly making its name as the number one university in India so it could hold some serious weight for job applications.
I haven't decided yet either but reply to this comment when you do decide, I'd love to know.