In terms of seniority, IMI New Delhi has more experience. The college has been around since 1981 while IIM Shillong is a newly established business school and also commonly known as one of the new IIMs.
Ranking and Accreditation
In terms of recognition in the US, both colleges have the same reputation and recognition abroad. While business schools like IIM Ahmedabad, IIM Bangalore and IIM Calcutta overshadow all the other business schools in the US.
Both IMI New Delhi and IIM Shillong have more or less the same reputation and recognition abroad while the former has AMBA accreditation as well. However, IIM A-B-C are well-known and respected more than these 2 institutions.