Both have that spy-fiction feel that reminds us of James Bond. To support that feel, they both have creative character designs; some good to look at and some ugly as sin.
They also have very good music composers who make those action scenes as groovy and smooth as a sarsaparilla(it's a rare drink, but it's good!)
They're basically moody shows, that are easy to take in, since they have American characteristics.
Big O has mecha, has an overarching story, has much better animation despite it's age, and has a strong message.
009-1 is orchestrated in a stand-alone manner, making it a bit harder to enjoy. It's character designs are also a little harder to swallow. And it also contains graphic content. read more
Both mix very good music with some very stylish action sequences. Both are episodic and don't really have an interconnecting story, and both were dubbed amazingly well.
As each episode tells its own story, some of them can be quite emotional, and some can be better than others.
But they both have graphic content, have elements that are targeted towards Americans, and are fun to watch now and then.
009 has more of a 007 approach to the stories, as many of the episodes reference the Cold War, deal with multiple countries, and feel a bit old fashioned. It also has a lower episode count, which could hamper the mileage of enjoyment
Cowboy Bebop has qualities that place it in the traditional sci-fi genre, making it easy to enjoy no matter how many times one watches it. It also has self-contained character stories, but they're anything but innovative. Unlike 009, Cowboy Bebop also has an abundance of insert songs which makes it's overall musical score stand out more.  read more
Both animes feature female protagonists and have a lot of kick @$$ action! Mylene Hoffman (009-1) is a cyborg spy who can dogde any bullet shot at her, besides that she can get out of any predicament (explosion) that life throws at her! Revy (Black Lagoon) is a hired hit-woman who fights with 2 guns in 2 hands, and she causes lots of explosions. BOOOOOOOOOOOOOOOOOM!!!!! Black Lagoon is a darker, sort of Underworld Gansta film-type television show. Meanwhile 009-1 takes a softer, yet more feminine James Bond movie type of series. Both are worth watching!
Both series contain strong female leads, futuristic setting and contain action scenes. Both are mostly episodic in nature, with one story not directly impacting the next (for the most part). Both follow leads that work for organizations that seek to fight crime, though 009-1 has more political implications. 009-1 is certainly darker and more serious in tone to Dirty Pair, which is more on the comedic side. 009-1 is also slower in pacing, and I couldn't really watch more than one episode at a time, while I ended up more binge-watching Dirty Pair.
I found Dirty Pair to be a satisfactory replacement for 009-1, as the settings and general way of story-telling are similar. read more
Both are serious "girls with guns" series with a heavy emphasis on style and mood. The main characters of both series can kill without emotion. Noir has very little blood or sex, while 009-1 has plenty of both.
Super cute assassin ass kickers that both work for a corporation. The action is raw and fast, although 009 is set in a more distant future than Madlax present day style. if youre looking for a futurisitic madlax this is a good start... good luck finding torrents for this one tho ~_~