While it's aesthetic gives the impression of a mystery thriller series, as much as it is that, the Big O is also a mecha series of the monster-of-the-week variety. Roger Smith, the main character is a 'negotiator' whose negotiations inexplicably end in giant robot battles, in a world where no one's memories of 40 years ago exist. One would have thought that written media and records would make it infinitely clear what had happened even if you lost all your memories, but the less thought you put into that issue, the better.
The series is obviously influenced by Batman. Roger Smith plays the part of Bruce Wayne, complete with a mansion, a butler and various gadgets, including of course his very own giant mech, Big O. R. Dorothy, his android sidekick, is a standout character. Bearing emotions of her own and greatly resembling a human, she's nonetheless animated as a robot with stiff movements and physical strength. The episode A Legacy of Amadeus, where she learns to play the piano in a more human way from an android teacher, sets her up as a character conflicted between her human and android identities.
The best episodes are self-contained stories. In Winter Night Phantom, Dan Dastun, who plays the part of Roger Smith's friend in the military police, confronts a string of terrorist attacks as well as his own memories. The episode plays up the series' parallels with film noir by itself having a final scene in parallel with a movie from Dastun's memory.
The main plot arc of the series concerns the search for memories of beyond 40 years ago, and informs the plot of every episode; whether it be a bad guy who uses newly found memories for infernal purposes (many such cases!), or Dorothy's struggle with memories inherited from the human she was modeled after.
This is where the Big O really struggles in execution. Despite many good one-episode plots, the overall premise still doesn't make sense, and many plot threads, particularly to do with memories, don't reach a satisfying conclusion, or indeed any such conclusion. It feels as though the series had more material planned, and looking at the production history makes it clear that is the case. Instead of wrapping things up in a satisfying way, the series goes with a bizarre exit plan that plays up the nature of memories as ambiguous, a miserly cop out that seems to be a reflection of the writer's inability to come up with a coherent ending.
That being said, I doubt The Big O would have survived 52 episodes without the mystery-then-big-monster-fight format becoming monotonous. As it is, The Big O a decent series with quite a bit more going on in art style and narrative than your average anime, but it will remain insubstantial in memory.