Given how I felt about the last book I read by Ms. Armstrong, I was wary about this one. However I really enjoyed this one.
It's detailed - it doesn't go extremely in depth into any one particular area because it's meant to cover all of the Crusades and tie in the history to more modern wars and conflicts in the Middle East and how it all boiled down (or over) into what we have today. But it doesn't gloss over anything either. She does a much better job of citing who she is quoting (recall that Ms. Armstrong is not an actual historian).
I think the major difference is time. Holy War is one of Ms. Armstrong's older works while The Bible is a newer book. I think she's dumbing down her writing (which was fairly passable early on) for the audience. Which is a terrible mistake in an author who is trying to write about history and religion and politics, etc. and make them accessible to a wide audience. It might work for a certain segment of the population, but for people who are actually interested in the history in more than a superficial way it's painful and aggravating.
There are some instances where she lets personal opinion enter into the book. For instance, there is one section where she claims that Christianity has done more harm to women than any other religion and mentions that she's 'proved this elsewhere'. She references an article she's apparently written, but I haven't read this so I can't comment on her proof. Another place she basically claims that expecting people to believe in the Real Presence in the Eucharist makes them stupid. Which...really, just take a look at all the great thinkers that the Church has produced and you can see that that's not so. But these instances are rare, and it's fairly easy to mark where she is speaking from her own thoughts and opinions and where she's taking about historical fact.
There's a ton of interesting information in there - the arrangements that have had to be made in the Church of the Holy Sepulchre so that the Christian groups won't fight over it is fascinating. Basically they had to give the keys to the church to the Muslims because the Christians couldn't share. Which is insane, but there you go. Oh! And when Omar conquered Jerusalem he was invited to pray within the Church of the Holy Sepulchre but declined because he knew that the ummah would want to commemorate the place he first prayed in Jerusalem by building a mosque on that spot and would destroy the church to do so. So he prayed across the street - and they did build a mosque there, and the Church of the Holy Sepulchre still stands today because of it.
Anyway. This book I would recommend. You can use it as a jump off point to get more into the history in specific details, since this is a more general work. But it can give you a basic overview of the Crusades.