The two shows are quite different, although on the same architect. The Art Institute show is mostly drawings and models, with some furniture, and emphasizes the architectural work in the larger context of the profession. A significant number of drawings (>100) are shown, as this show describes the innovations in the architectural work and provide an overview of the entire career.
The show at the Arts Club is a more intimate and personal look at the person, the inspirations, and the oddities of his work - and looks at furniture, jewelry, fabrications, photography, patents, and other architectural works designed by Goldberg. It is a more multi-faceted show, less professionally oriented tho.
It is recommended that one see both: the Arts Club show is intended to complement the Art Institute show. Both are serious endeavors and done with a lot of care. The press releases on both shows can be found on this site - go to News and Events.