"Heaven's War" is a great book in the tradition of pulp stories of the early 20th century. Nothing wrong with that. It is definitely not hard science fiction. Nor is it in any way comparable to "Rendezvous with Rama" other than the basic premise of an extra-solar object with a cylindrical habitat inside. While the story is totally unnecessary, the storytelling carries the reader along at a reasonable pace - although it is sometimes hard to say whether it is trying to be satirical on purpose (or not).
Mild spoilers from "Heaven's Shadow": along comes an asteroid in 2019 - apparently from outer space - of about the size of Rhode Island. Since its course brings it pretty close to earth, two (competing) missions are sent for a visit. The exploration quickly turns into a rescue mission by the teams' own faults, only to be interrupted by cold-war type politics which leads to a detonation of a briefcase sized nuclear bomb. In the meantime, the near earth object sends some magical bubbles to pick up a few hundred people from earth and drop them off inside the habitats before making its way out of the solar system again.
More spoilers: In "Heaven's War" we now have to deal with and follow the people around the asteroid. What really makes this book a worthy sequel is the basic structure of the story which in itself is completely bootstrapping. Every problem that has to be solved by the human passengers is in fact only created by those same humans coming on board - at one point this is even explicitly said. While it is said that mankind (or some "volunteers") are supposedly needed to help in a galactic war that threatens everything, it seems that their main purpose is to name things. There are Architects, Revenants, Reivers, Sentinels, and a few other creatures or things that try to be deceptive. And there is a Prisoner, which so far is lurking in the background.
While there are almost two hundred people running around, the main part of the story is carried by two teenagers. Since it is not clear why any of the people was picked up, it doesn't matter anyway. Everyone is more or less left alone to their own sweet things. So, people start to wash in their drinking water reservoir which is more of a mud pool to begin with. Alternating days for men and women, of course. The gay guy naturally thinks about his chances of sexual activity first and foremost. Other people find a "machine" that produces food, which is good because an asteroid typically does not contain much soil. The general attitude can be described as optimistic defeatist, I guess. Which is: we're stranded on an asteroid and being kept alive by technology that we don't understand, so we might as well just try everything without much thinking. The food may be poisonous, but if one doesn't try it people have to starve after all - which means starting with small samples wouldn't make sense either...
Then there are the Revenants, reproductions of dead people whose main purpose is to convey the story of the Architects to humans. I don't know if the authors thought this was a neat trick, but it sure carries the heavy weight of a deus-(information)-ex-machina. Whatever mystery remains, the Revenants just have an answer. Already in the first book they are used as a point of view, so they apparently have to be trustworthy. There is a revenant dog (and a cow) - purpose unknown other than luring the mentioned teenagers into a pitch black tunnel.
It all could be fun if it wasn't for the recurring attempts of throwing in some sort of physics that we know. Gravity is obviously very low on the asteroid, but on the inside there are spots of dense gravity. Maybe again a neat idea by the authors who thought that anti-gravity was too far fetched here, but even introductory analysis tells you that you have to integrate this properly in space. The asteroid is an extra-solar object and obviously very fast when is swings around, but it can easily break into an orbit around earth with just three "eruptions" while people are on its surface. There are gelatinous space suits which magically carry sound waves through vacuum, no questions asked. The overarching threat for the universe is information that is not changing - sounds catchy but I suggest a simple search for entropy and rework this section a little bit.
Of course, this is a work of fiction, but at least it should be self-consistent. And while there is a little bit of mystery in the story, it completely lacks any sort of wonder. Whatever is thrown at the human characters, they instantly forget everything they ever learned or experienced in their lives so far and come up with an explanation it. Technically, the writing seems to be following every rule of a successful novel canonically- except this one last important thing: every now and then break the rules. The biggest question remains, whether the concluding "Heaven's Fall" will add anything in terms of an underlying crisis. In summary so far, the Architects stopped by earth to pick up humans because they are faster thinkers who then rely on alien advanced technology to solve problems that they themselves created in the first place.
This book doesn't hurt. Does that alone justify an initial hardcover edition already?