We get into this when we discuss the Big-Endian/Little-Endian controversy in the Lilliputian "Character Analysis." Check it out!
The Lilliputians and the Brobdingnagians
See our "Character Analysis" on the Brobdingnagians for a few thoughts on this comparison.
The Brobdingnagians and the Laputians
These two peoples aren't much alike, but they do share a couple of interesting contrasts: first, the Brobdingnagians favor practical applications of science over abstract theories. The Laputians have their heads both literally and figuratively in the sky. Second, the Brobdingnagians favor clarity of language. The Laputians care so little for the meaning of words that one of them is trying to produce a book using a rotating wheel to pick phrases at random.
The Brobdingnagians are Gulliver's favorite Yahoos; they're still human, so they're not perfect, but they're not as bad as some. If they are models of good behavior, then their focus on practical science and clear writing provides useful background for understanding what's wrong with the Laputians.
The Brobdingnagians and the Houyhnhnms
In many ways, Brobdingnag provides the dry run for Gulliver's experiences with the enlightened horses of Houyhnhnm Land. It is in Brobdingnag, that Gulliver first begins to realize how tiny and insignificant he is in the grand scheme of things, a discovery that really hits home in Part 4. His initial introduction to Brobdingnag creates one essential difference and one key parallel between the Brobdingnagians and the Houyhnhnms.
First, the difference: when Gulliver is introduced to Brobdingnag, he is found by a farmer who realizes that he can make a huge amount of profit if he shows a tiny man like Gulliver at market days. So the farmer, Gulliver's master, sets out on a tour of his giant country with his giant daughter and tiny Gulliver. Gulliver finds it incredibly exhausting to perform on order like this, and he starts to worry that he is going to die. This farmer becomes so caught up in his own greed that he works Gulliver nearly to death for profit. The Brobdingnagians have a taste for luxury much as Europeans do. This prevents them from achieving the kind of balanced life the Houyhnhnms model.
At the same time, there is still a key parallel. Gulliver's transformation into a kind of freak show punctures all of that self-importance he learns in Lilliput. In Brobdingnag, Gulliver gets up close and personal with the experience of being totally at the mercy of others. His eventual status as a cherished pet of the Queen of Brobdingnag and her helper, Glumdalclitch, does seem to prepare the reader (and perhaps Gulliver) for his eventual happy service to the Master Horse in Houyhnhnm Land.
Another intriguing parallel is their commitment to avoiding violence: the Brobdingnagian King refuses Gulliver's gift of gunpowder, and the Houyhnhnm Master Horse does not understand the meaning or purpose of warfare. We can compare both of these groups to the warmongering Emperor of Lilliput, who comes to hate Gulliver for not helping him enslave Blefuscu.
The Yahoos and the Houyhnhnms
This one is the big contrast of the book – please see our "Character Analyses" of the Yahoos and the Houyhnhnms for more on this topic.