Summary: These two excellent works complement each other nicely to give an overview of Iraq with a focus on the recent war.
I'll start with the former. Fiasco's main strength is that it is an extremely detailed and well-written account of just what happened to bring the US to war and how the occupation was carried out. The 2003-2004 period is most damning. It was as if Sun Tzu, Clausewitz, Napoleon, Lord Nelson, and Eisenhower had been set on a panel with the express purpose of designing a strategy to fail as utterly as any in history. The unbelievable stupidity and incompetence of the high command, both military and civilian, is distinguished from the performance of the actual soldiers, which mostly seemed haplessly unprepared for the conflict they were dumped into, but tried to make the best of an impossible situation. Later, after some shakeups at the top command, techniques that were at least in the same galaxy as sanity were implemented with some positive effect.
However, I struggled with the book's essential sympathy for the nation building project. Ricks details the more successful efforts of leaders like David Petraeus and H.R. McMaster, who were able to understand and implement better tactics for fighting an insurgency and building a country. I summed it up in my own mind as 2/5ths Marine Corps, 1/5th Army Corps of Engineers, and 2/5ths Peace Corps. This and the catastrophic yet easily avoidable mistakes at the beginning of the war combine to make an account that in many respects doesn't discredit the doctrine of pre-emption (indeed, Ricks explicitly states he could still support such a policy in the right circumstances), but rather tries to salvage it. I have to grudgingly admit that Ricks' account convinced me that such things are possible in theory, but he doesn't really grapple head-on with the policy issues raised by the doctrine of pre-emption.
Tripp's book, on the other hand, gives that broader perspective. It is a serious academic work, a kind of shallow overview for the nonspecialist or historian looking for a place to start deep research. It's a bit of a slog at times, but worth it for the overarching narratives that were driving a lot of what happened during the US invasion that Ricks, buried deep in the details, misses. Iraq's initial boundaries, a relic of the collapse of the Ottoman empire based entirely on political convenience, are described in the context of the British colonial action after WWI. The long history of monarchy and of increasingly violent coups by military leaders is followed, logically ending with the ruthless Saddam Hussein. The American occupation is given the same kind of treatment as every other Iraq regime, and tied into the narrative threads of the previous history, something the Ricks does not do.