The overall story arc is the same, thankfully. And covers the first 6 books. The societies, politics etc are more or less spot on. I loved the detail they had transferred to the screen about how dangerous and harsh life is out in the solar system. The characterisations suffered quite a bit. (Strangely except Bobbie, and Amos) Some characters in the books never appeared in the series, and some became a blend of others, especially Drummer, but actually that worked. They also narrowed the timeline down a lot, in the books travel between the stations, rings and planets takes months, even years. No mention of this strain, especially during battles, when you could have a week knowing there was a pile of missiles coming your way etc. Also most crews are on anti aging meds, which slow aging but not stop it, and they do mentally age, as in become tired, this is well drawn in the final three books.
All in all there are a lot of faults in the series, but the books are dense, (as in very detailed.) and to be honest the adaptation has been a hell of a lot better than many other book to Film/TV