Nope you don't get to pick your campus, but they do take a preference - but ultimately it is a random allocation
Mohali is a smaller and newer campus and is not a main city. Total students are only 200 - 250 so you tend to know almost everybody and it's a well knit group.
Hyderabad is the bigger and legacy campus, so more people want to opt for that naturally. There are almost 700 - 800 folks on campus so it's impossible to know everyone
In terms of faculty, there isn't a lot of difference - ISB tries to standardize it to the extent possible. Your campus doesnt play a role in placements either, it's not really revealed to companies what campus you are from and even if they were to find out, there isn't really a preference for any campus