Daimajuu Gekitou: Hagane no Oni

Both anime deal with a powerful life form attacking humanity and the main protagonist must use a powerful mecha to save humanity from danger. They are also both action-packed anime with similar atmosphere and a similar vibe. Biggest difference between the two is that Demon of Steel is older and is only a one shot OVA that is 56 minutes long while Nenon Genesis Evangelion is a TV series and was released 8 years later. If you like one, you should enjoy the other.  

"Genocyber" and "Demon of Steel: Battle of the Great Demon Beasts" / "Daimajuu Gekitou: Hagane no Oni" are mature sci-fi anime that involve powerful monstrosities destroying humanity. The violent action scenes of these two works both involve modern militaries and create similar atmospheres of terror. 

"Akira" and "Demon of Steel: Battle of the Great Demon Beasts" / "Daimajuu Gekitou: Hagane no Oni" are mature sci-fi anime that surround a violent clash between two formerly close friends who now stand on opposite grounds. The action scenes of these two works both involve modern militaries as well as supernatural monstrosities that began to demolish human civilization. 

Huge monsters of mystical origin fight against each other. The monsters joint forces with young men. A girl is in love with one of them. Between the fights is a lot of talk. 

Both anime are created around the same period (late 1980's-early 1990's) with similar animation and a similar vibe. The main protagonist in both anime uses a powerful mecha suit to stop a evil monster from destroying humanity. If you like one, you should enjoy the other.