So... is Juu Ou Sei finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: June 23, 2006
Manga finished: January 01, 2003
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
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Synopsis
Juu Ou Sei tells the story of twin brothers, Thor and Rai, who are exiled to the dangerous planet Chimaera after their parents are murdered.
To escape Chimaera, they must become the "Jyu Oh Sei," a ruler who unites the planet's warring factions, known as Rings.
Thor, driven by the need to avenge his parents and return home, embarks on a perilous journey to survive the harsh environment and navigate the complex political landscape of Chimaera.
His quest for survival and power intertwines with the mystery of his parents' death, slowly revealing a deeper truth about humanity's place in the galaxy.