The manga is...different. Hitoshi Ariga was brought on to do the adaptation but wasn't given an incredible amount of material to work with (he wasn't even told the Big O was black) and freely admits he never knew what to do with Dorothy.
It follows a different path from start to finish. Because the serialization began before the anime, he waited three chapters to introduce Dorothy (rather than spoil her introduction). Beck is the primary villain in the manga for most of the run, with Schwarzwald and Angel following close behind. The Rosewaters are far less involved.
The manga also ran longer than the TV show, with its original run lasting until 2001. The final volume is something of a prototype for the finale of season 2, but also vastly different (fitting the different characterizations). During Season 2's airing on TV in Japan, he also wrote another manga, Big O: Lost Memory, set before Volume 6 of the first manga. That one's never been licensed.