How does the common law concept of "fair dealing" in Australia generally differ from the statutory and case law concept of "fair use" in the United States?
There's very little difference. Fair dealing only applies when use of a work for specific purposes does not infringe copyright if the use is only for criticism, parody, news reporting or research; and does not affect the commercial value of the work. If a reproduction of work is used, it is limited to 10% or a single chapter (dependant upon length). Aust Copyright Act
The reference to fair use appears to be the same thing, although there is no reference to parody or satire. US Copyright Fair Use