.

.

Enemy With Prominent Legs

Both series have an enemy that has extremely long legs, that are the only part of the enemy visible at first.

RahXephon

Evangelion

Two Old Men Play Shogi

Two people can play Shogi in any anime, and it doesn't necessarily mean a connection. However, the similarities in RahXephon and Evangelion are that the two people playing Shogi are both old men, one of which is a professor, one of which has a secret agenda, and that the game of Shogi may symbolize the false friendship and hidden tension between these two men.

RahXephon

Evangelion

Shogi

Shogi

In both series, it is revealed that one of the older characters was actually a professor in his younger days. This revelation, although seemingly minor, is treated as somewhat of a dramatic plot twist by both shows.

The scene when Elvy is reprimanded is taken directly from Evangelion, scene-for-scene.

It's only reasonable to assume that if a character disobeys orders, there will be a scene where he/she gets reprimanded for her behavior. However, observe how identical both of these scenes are:

"It is against regulations to act on your own."

"You're going to lose your life that way." 

"It's my life." 

"If you pilot with that attitude, it'll kill you."

"I don't care"

In both series, at about the same point in the timeline, the character has a promotion/transfer, and a party is thrown to celebrate it.

In both series, a pilot has the same motives for piloting. Ayato pilots because it makes him feel connected to other people. Rei pilots because it makes her feel bonded to other people.

The character Futagami from RahXephon is a clone of Kaji from Evangelion. Both men are secretly spies, have a laid-back disposition, usually have wide, smug smiles, and both also possess stubbles. Futagami simply looks and acts just like Kaji does.

Both men are also involved in scenes where a gun is being pointed, and the camera pulls away just before the gun fires.

In both series, high heels represent womanhood. in Evangelion, Kaji knew Misato before she wore heels - meaning when she was not yet a woman. When Misato drops her heels while kissing Kaji, it symbolizes her fall from womanhood back to being the girl she once was. In RahXephon, Megumi yearns to reach adulthood and become a woman, and tries wearing high heels, but fails, because she is still a girl.

In both series, the Misato character is a woman of high rank who puts on a serious face at work. But, as is revealed by her own actions and other characters' words, at home, she is girlish, silly, and sometimes a slob.