In the Automotive Industry, the biggest names are UG, CATIA, and Pro-E. I would guess the decision to use one package over another really depends on a decision from the management and was made many years ago. Large companies are not usually willing to invest the huge resources into changing from one package to another due to the massive training required, restructuring their Data Managment system/procedures, and possible problems with legacy parts.
In regards to using the same package as your customer/supplier, I disagree. From my experience, even if our main core CAD package is the same as our end customer, we will only send them a converted to native language STEP/IGES packaging envelope to remove all of our proprietary technology and the CAD structure tree. We will never send them a raw native langage part. We keep basic seats of the other packages only to make sure the translation goes correclty when we deal with stubborn customers that demand files in their native language (non Step/IGES format, but must be UG, CATIA, or Pro-E).
-Ryan