First of all, I love the style of Big O. Apart from its terrible name and opening song it showed a lot of promise in the first episode. It was a great idea, too. I liked the pacing and the 1992 animated batman look. It is an entertaining anime, light hearted fun (though it didn't have to be light hearted, but taken otherwise is a mistake. It is intended to be serious, but there are just too many flaws and odd things happening).
On to the music. It is not good, atmospheric or otherwise, but the opening and closing songs really take the crap
cake. As for the characters and dialogue, they are also not good. You are never really convinced that Roger puts on a good facade as a negotiator. Pretty much all the characters are weird in some way and it is hard to think of them as very real characters in this world. What was really annoying though was all the misguided Christian symbols and the Christmas episode. It just added more weird crap to an already weird anime. And don't misunderstand me, I like weird things, when I say this is weird I mean inconsistent and full of unexplained illogical phenomena. Anywho, it is worth a watch if you like the look of it, just don't expect a great story and deep character development. And please for the love of god, make no comparisons to Cowboy Bebop. It is not even on the same plane of existence.