What is the closest thing to a class or type in RESTful systems?
I think it is the media type. URIs name resources, but don't describe types. Media types, on the other hand, describe representations. A representation is the closest thing to an object. Media types describe types of representations.
That's why, the more specific the media types are, the better. Using a generic type like application/xml is like using a generic class like java.lang.Object (or its equivalent in other languages).
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Doesn’t that trip up clients like XHR that count on an known XML media type to recognize and parse the XML document?
Not necessarily. XHR can recognize XML-ish content-types ending with +xml, such as application/atom+xml, application/mystuff+xml etc.