What social differences are exemplified by the contrast between Gatsby’s mansion and that of the Buchanans?

The differences between the Buchanans' home and that of Jay Gatsby are meant to exemplify the social barriers that separate old money (inherited, established wealth) and the nouveau riche (newly earned wealth).

Tom and Daisy's house is described as a "red-and-white Georgian Colonial mansion" with "French windows"  an "Italian garden" and a stable for Tom's polo horses. Georgian architecture utilizes design elements dating back to ancient Greece and Rome and later revitalized in the Renaissance...

The differences between the Buchanans' home and that of Jay Gatsby are meant to exemplify the social barriers that separate old money (inherited, established wealth) and the nouveau riche (newly earned wealth).

Tom and Daisy's house is described as a "red-and-white Georgian Colonial mansion" with "French windows"  an "Italian garden" and a stable for Tom's polo horses. Georgian architecture utilizes design elements dating back to ancient Greece and Rome and later revitalized in the Renaissance and neo-classical periods. Tom and Daisy's house is meant to represent tradition and the security of time-honored, classic design that suggests European refinement. Polo has long been called "the sport of kings," only indulged in by the elite. Tom and Daisy are members of the old money establishment.

Gatsby's house represents his nouveau riche, socially-aspirational status. In a bid to capture some European prestige, the house has been designed to replicate a French country hotel. Its size and scale make it impersonal (like a hotel) and the "thin beard of raw ivy" suggests a recent attempt to make the house look long-established like the estate of an old money family.

Fitzgerald, F. Scott. The Great Gatsby. Charles Scribner's Sons, 1925.