All three books (Iyov Mishlei and Tehillim) are written in a complex poetic style. The separate trop represents the shift from prose to poetry and may have been sung in a more songful manner than the regular prose trop. A proof to this distinction lies in Iyov, whose first, second and final chapters are written in prose and have regular trop.
EDIT: The structural difference between the prose and poetry parts of Iyov can be seen in this clip from the Aleppo Codex (Keter Aram Tzova) showing Iyov 2:11 - 3:6. Notice how once it switches to poetry, the text is split into two columns reminicesnt of the way Ha'azinu is written in a Torah. This pattern extends through the poetic sections.