I've done a quick study of this at my office, and I'm not saying the results were what you experienced, just that this was one sample. When people put the same simple search term in both, they found the result quicker in Bing. When the search term was more complex and used operators, they found the result quicker in Google. The difference I saw was that people were used to Google and how to format a search so Google finds it better. The same search operators didn't work as well in Bing.

Whether this is a problem with complex queries in Bing or a problem of the computer training the user, I can't say. This was just what my office found out. For the record, no one changed their search provider.