A top tier consulting firm might be looking to very different kind of profiles, depending on its needs or on the trends of the market.
At that level, I think the applicants that impress them the most are the ones with an excellent GPA and an internship experience in a very selective company. Due to the short length of an internship it is rare that the person is able to develop a deep expertise in the industry or the business area covered so the consulting firm would prioritize the ones that successfully went throguh a selection process that is similar to the one they have. This can be considered a good benchmark for how the candidate will perform in the interviews and, eventually, on the job. The first kind of companies that come to my mind are Investment Banks and other top tier consulting firms but there are several others (like the Googles or Apples even thoguh I haven't found many people that switched from those companies to consulting).
A different case can be made for people that spend 2+ years working, in this case it can be highly regarded also someone who doesn't have a top tier employer name on his / her CV but that developed a significant expertise in a specific topic, say operations.