Witness the true beginning of the Matrix: how men created the machines and how those machines stood up against their masters, and the effects of the great war that waged between them, which in the end led to the fall of mankind. Watch the ship Osiris and its efforts to warn the remaining humans of the imminent attack; follow a champion who happens to break free from the Matrix; explore the exploitation of a glitch in the overall system; observe the story of the Kid and how he was found by Neo; travel with an investigator who tracks the well-known hacker Trinity; and learn the secrets of the Matrix in other wondrous ways.
A girl on the subway listens to music, a boy on his skateboard zooms down the streets, and a motorcyclist picks up his date while the buildings of the city both sprout anew and collapse all around them. Fast-paced, always-moving and ever-evolving, follow a group of people in their daily lives while the cities around them develop to the point of self destruction.
Follow interstellar bounty hunters Spike Spiegel and Jet Black as they scour the galaxy for criminals with prices on their heads. Hoping to escape their past, they live on the spaceship Bebop, but it's a dangerous business and old enemies don't forget easily. Allies come from unlikely sources, however, as they find comrades in the beautiful swindler Faye Valentine, the genius child hacker Ed and the genetically engineered 'data dog' Ein. Will they be able to help each other though their respective struggles, or is their fate really inevitable?
In a broad range of sci-fi type animes i personally think that both are some of the best out there. Cowboy bebop with its captivating scenes in outer space and symbolic storyline and the animatrix with its deep ideas relating to the matrix trilogy, both truely stunningly epic proformances.
In the future, androids live side by side with humans – but not as their equals, as their slaves. Though they look identical, these androids must display a holographic ring over their heads so the difference is clear. One day, a boy named Rikuo finds abnormal activity patterns in the logs of his own android, and alongside his friend Masaki, he sets forth to find where the android has been. Much to their surprise, the duo discovers a secret café known as Eve no Jikan with a single rule: within its walls, there must be no discrimination between humans and robots. In this place, androids appear to be human and are even displaying signs of independence – a trait that should not be possible. Rikou finds his perceptions increasingly challenged as he struggles to come to terms with his own android, and the relationship between man and machines...
You will like one if you like the other, both involve Sci-Fi aspects as well as machine sentience, where Animatrix emphasises the worst possible outcome being the war between man and machine, Time of Eve focuses on the relationships between man and machine if machines were able to achieve free will.
Naota Nanbada is a boring young boy who leads a boring life in a boring town. His older brother has left for America, and the closest he comes to any excitement is when his deadbeat dad has too much sake. But things change one day when a bizarre girl zooms up to him on a scooter and smacks him in the face with her guitar. What's more, once Naoto returns home he discovers that this strange woman has arrived ahead of him and moved in! Not only does she constantly engage in perverted activities with Naota's father and flirt with the young man himself, but she also claims to be an alien who is searching for the ‘Pirate King.' Now, Naota must learn to live with this new intruder, deal with an odd government agent who sports exceptionally large eyebrows and the mysterious Medical Mechanica, and come to terms with the fact that there are a variety of robots and weapons emerging out of his head - amongst other things. Perhaps boring wasn't so bad after all...
FLCL and Animatrix adjoin insanity and atmosphere of rational lunacy. It's especially noticeable in the Beyond and Matriculated episodes of Animatrix. The Matrix and the flat-iron shaped factory give us a sense that something bigger that exists behind the scenes.
By the year 2085, World War III has left both the East and West crippled and destroyed. The major cities have been reduced to rubble, and a mechanical army known as the MME - soldiers originally created by both sides to fight in the war - has decimated the population; extinction is eminent. Though hostilities prevent the two groups from cohesively joining together to combat their now common enemy, a daring plan has been hatched that may save some of the world's population from destruction: they will be sent to the Mars Base in an evacuation. Sandy Neuman, along with other remaining military forces, must now fight the machines with all they've got so that others may escape safely to the stars...
As a caveat, Animatrix is better than Rhea Gall Force in almost every way - animation, story, and overall enjoyment. Regardless, this is a decent rec based upon plot alone. Both deal with a future where machines are winning the war against humanity, and that alone makes an acceptable recommendation.