Following a disastrous event known as "The Second Impact," humanity teeters on the brink of extinction. Having not completely eradicated mankind previously, creatures known as Angels begin attacking once more in an attempt to create a third, and final, catastrophe which will annihilate mankind once and for all. When conventional weapons fail to stop the Angels, however, the Japanese military organization NERV proposes the use of strange mecha called Evangelions. When the first Evangelion rejects its pilot, though, NERV's commander is forced to draft his estranged son, Shinji, as mankind's savior. Bitter of his father's estrangement and insecure in his abilities, Shinji struggles to overcome his doubts and fears in the face of certain death, but ultimately continues to fall short despite his efforts. As he slowly improves his skills, however, he must come to terms with the greatest question of all: is humanity worth saving after all?
Ayato Kamina may seem like an average boy in a devastated world, but after being captured by TERRA, a military organization set on saving the world from the Mu, an alien race set on "tuning" the world, he realizes he is an instrument in deciding the fate of humanity and piloting RahXephon. Not only is Ayato the only person who can control the mecha, but he also has a terrible fate of his own. Holding onto memories of his old life and grasping to keep his own humanity, he must struggle in this new world and realize his true potential with RahXephon.
Both mecha shows have a lot in common apart form their respective eponymous mecha. Both can be rather obdurant, making casual viewing a bit annoying, and there are conspiracies left and right, nebulous organisations and large casts full of people that really are too young to be in a military context. The mecha designs are rather similar, and the enemy designs are pretty out there.
There's a larger mystical theme (Christianity in EVA and musical terms in RahXephon) that serves to set them apart from a lot of other mecha anime — but obviously not each other. People that like one of these and want a similar viewing experience would do well to check the other one out.
As the mighty star fleet of the planet Keron prepare their invasion of Earth, Sergeant Keroro and his elite team of commandos have been sent to infiltrate the enemy strongholds and gather as much intelligence as possible. However, it seems even his extensive military training is no match for the forces of Earth, as he is discovered and captured by the two middle school siblings, Fuyuki and Natsumi. Submitted to the rigorous torture of housework duty, the amphibious Keroro must now bide his time, covertly locate his squad-mates, and resume his mission of conquest!
If you liked SGT Frog or Evangelion you'll like the other because most of the human characters in SGT Frog are parodys of Evangelion characters. Fuyuki is a parody of Shinji and Natsumi is a parody of Asuka and Aki is a parody of Misato and so on. There's also an episode where they Evangelion itself as well as the characters. By the way it should be noted that SGT Frog is intended to be watched by children and Evangelion wasn't though that shouldn't hinder you from enjoying ether show.
"I have only abandoned my body, I still live here" - are the words emailed to friends of Chisa, several days after her death by suicide. As Lain delves deeper into the world of the "Wired" (also known as the internet), the line between it and reality becomes more and more unclear. Close the world, open the nExt.
Simon lives a boring life in the underground village of Jeeha, where his main job day in and day out is to dig tunnels. His close friend Kamina, however, longs to bust out of their oppressive existence and reach the surface world where open skies and adventure await! One day, during his usual digs, Simon discovers a robot with a big face buried amongst the rocks. No sooner has he shown Kamina his mysterious find when two beings from the surface crash land into Jeeha Village - one is a gun-toting woman calling herself Yoko and the other is a terrifying mecha piloted by a Beastman! Seeing their chance to escape village drudgery, Kamina rallies Simon and Yoko to defeat the invader using their new robot, Lagann. However, upon breaking out onto the surface world, Simon, Kamina, and Yoko encounter enemies more powerful than they could have envisioned. Their fight for adventure just turned into a war for the survival of the human race - will their lust for freedom hold out against such terrible odds?
Though quite different shows, I feel both will appeal to the same viewers due to mech of epic proportion, dystopian backdrop, and crisp art styles. Both utilize computer graphic editing in such a way that it isn't overtly obvious as in many anime of similar genre.