Zoids Genesis

This is the first film in the Rebuild of Evangelion film tetralogy, a series in which Hideki Anno has revamped Evangelion into a story that's less psychologically intense, and is easier overall to understand than its parent TV series. This particular film is nearly identical to the first six episodes of the TV series, just on a much higher, Hollywood style budget. The two currently released sequels (2.0: You Can (Not) Advance and 3.0: You Can (Not) Redo) are where it deviates from the original series' overall plot. However, many of the reasons I found the original Evangelion similar to Zoids: Genesis are still intact: Living Mecha, Post-Apocalyptic World, and some really dark scenes. Like the original, Rebuild of Eva takes place in the year 2015, 15 years after an event called "Second Impact" destroyed half of the world's population, much like the Great Cataclysm in Zoids: Genesis did to Planet Zi. Now, in the present, towering alien monsters known as "Angels" are attacking the fortress city of Tokyo-3 to try and initiate Third Impact, which would wipe out the rest of the life on Earth. To combat them, the UN backed organization, NERV has built giant cyborgs known as Evangelions as the last line of defense. Shinji Ikari is called to Tokyo-3 by his estranged father and Commander of NERV, Gendo, at the same time as the attack of the Angel "Sachiel". Gendo coerces Shinji into piloting the untested Evangelion Unit 01, and much like Ruuji was able to activate Murasame Liger, Shinji is able to do so with Unit 01. Compared to the original series, though, Rebuild is a little more lighthearted, especially in the second film, where the interactions between Asuka and Shinji are reminiscent of some of the comedy that cropped up in Zoids: Genesis. read more 

Another mecha series with a rebellion against an oppressor, Gurren Lagann is a Super Robot-style mecha anime like no other, far more wild than Zoids. Simon and his foster brother, Kamina, wish to escape their underground village and see the surface. Mankind has been driven into these kinds of villages by the Spiral King and his mooks, known as Beastmen. They get their chance to get out of there when a gunmen (as the series machines are called), falls into their village during a fight with Yoko Litner. Yoko's extremely powerful rifle has no real effect on the thing (neither does Kamina's sword, for that matter, but he's lived under a rock for years almost literally, so we can forgive him.) But just earlier that day, Simon had unearthed a ting gunman that they decide to call "Lagann" Apparently operated via fighting spirit, Simon defeats the beastman with Lagann, allowing himself, Kamina, and Yoko access to the surface. When they meet up with the rebellion group that Yoko is a part of, Kamina manages to get his hands on another gunmen, which he names "Gurren". After learning about the issues with the beastmen and the Spiral King, Simon, Kamina, Yoko, and one of the other rebels, Leeron, set out to do the impossible, see the invisible, kick reason to the curb, and FIGHT THE POWAH! read more 

Like Code Geass, Zoids: Genesis involves a young boy who is wrenched straight from his everyday life and is drawn into the conflict between a major military power and those who oppose it. Both characters go on to become major leaders in the resistance movements. Ruuji Familon lives a quiet life in the village of Mirodoo, until, just after they have raised a large Zoid from the depths of the ocean, they are attacked by the vicious Bio Zoids of the Digald Empire. The Zoid they just raised, Murasame Liger, selects Ruuji as its pilot. 

Fight with big animals, dragons or robots, similar world and story.