What is the difference between the society of Lilliput and the society of Brobdingnag?
The first major difference is physical. The Lilliputians are very small and consider Gulliver a giant. The Brobdingnagians are huge, and Gulliver appears tiny in comparison to them. These size differences lead to many of Gulliver's more humorous adventures.
Next, the society of Lilliput is extremely competitive and quarrelsome, obsessed with debates over trivial differences such as those between the Low-heelers and High-heelers and those between the Big-enders and Little-enders, who differ over which end of an egg should be cracked. This is intended to satirize the political and theological disputes of Swift's own period.
The Brobdingnagian society, by contrast, is peaceful and well-governed. Their laws are clear and simple, and the focus of intellectual effort is not on theology or metaphysics but on things which directly benefit people, such as medicine, history, economics, and the arts.
Although both societies are, like Swift's own, monarchies, in Lilliput power is wielded capriciously and in Brobdingnag philosophically.
The Lilliputians are very warlike while the society of Brobdingnag is quite peace-loving and gentle, especially in comparison to the society of Lilliput. In Lilliput, terrible wars have been fought and thousands have died over disagreements about which side of the egg should be cracked: the big end or the small. The emperor of Lilliput becomes angry with Gulliver when Gulliver refuses to decimate the Blefuscudian fleet or participate in the enslavement of the citizens of Blefuscu by the Lilliputians. Ultimately, he charges Gulliver with treason and plans to put him to death for his supposed crimes against the state.
The ruler of Brobdingnag, on the other hand, recoils from Gulliver and pronounces his countrymen to be the most hateful race of vermin that has ever inhabited the world after Gulliver tells him all about their society and military and politics. This society is much more peaceful than Gulliver's and the Lilliputians'.