There are two chips on ethernet shields - the one on that shield and the W5100. The W5100 incorporates a lot of functionality that the library does not have to. The ethernet library does not work with that shield, although there is work in progress to make a library that provides all the same functionality, in an easy to use format, as the standard ethernet library.
For now, though, you are better of spending the extra money for a W5100 based shield.