The neoclassical values reason, the intellect, the rational, order, balance. The term is used somewhat synonymously with the Enlightenment and the Age of Reason. Neoclassicism recaptures the values of Ancient Greece and Rome. This is an age of great satire and the age of the essay. Swift and Pope wrote during this period.
Romanticism is a strong reaction against this. Romanticism values intuition, the spiritual, emotion, imagination, creativity, spontaneity, self-expression. Romanticism points back to the Middle Ages, rather than to the classical. This is the age of lyric poetry. Woodsworth, Byron, Keats, and Shelley were romantic poets.
This is, of course, a simplistic breakdown. These movements or periods are extremely complex. And I don't know why they valued their parents during these two periods.