I think you should ask HHL to put you in touch with an Indian student. It's hard to work part-time while taking a full-time course and learning the language. I don't think the Mannheim MBA is world-famous. Both of them are comparably-strong European business schools, with a three-year average ranking of #26 for Mannheim and #33 for HHL.
http://rankings.ft.com/businessschoolrankings/european-business-school-rankings-2014 Mannheim does better in the full-time MBA ranking because it's more oriented towards finance and consultancy, while HHL is famous for entrepreneurship. As a result, HHL is lower in the MBA rankings because of the lower salaries that entrepreneurs have initially. Mannheim is also better known because it's part of a large university with a big undergraduate programme. I think HHL has advantages because of the US-style two-year experience, which is much fuller, and especially that it gives you more time to learn the culture. That said, Mannheim is a richer city and a more cosmopolitan one.
There have been some comments on the board in the past about racism in Germany. I am sure you can search and find them. Considering that students spend time in the centre of the city, I am not surprised that I've seen no reports of specific difficulties. If you were to go out into the suburbs, or into smaller towns, then an Asian is certainly an oddity as a European or African person might be in a small town in India. But if you don't go alone to the sort of places where most German outsiders would not go alone, then you will be fine.
PS It occurs to that me the big different is that HHL, HSG, Mannheim and WHU are the leading schools in the German-speaking region, which has 120 million people and is one of the richest in the world. In the case of UIC and SUNY Buffalo, these are not even the leading schools in the state, or arguably even within the state university systems in those states. The quality of the students and faculty you would get is much higher at one of the top two or three schools in any large Western country, and these are schools which were born global, rather than born to serve one province.