Ashoka University is a far better choice than institutes like NMIMS and Symbiosis. Yes, it's a fact Ashoka has short existence when compared with the other two institutes.
Ashoka University is entirely on a charitable drive by the group of big reputed entrepreneurs who motivate to make a radical change in the history of the Indian college education scenario. It focuses on better education rather than money-making students.
Symbiosis and others can not match Ashoka's record as you can see its alumni are in top companies. You will get good opportunities and exposure in Ashoka than in other institutes. Co-curricular activities and sports are the best part of the student in the institute, as you see in brochures on the website are the same.