Boukyaku no Senritsu

Half the staff list, that's the similarity. Hence the same aestheticism, surrealism, mixture of reality and fairy-tale... Main characters are also pretty similar, and some images and devices from Utena have been reused in MoO. Only MoO has much more parody and fanservice elements, but still it's a must-see for Utena fans. 

It's strange. When I watch both of these series, either title just pops into my mind. They definitely have a few similarities least to say coming from that: Both series has similar artwork Both series has themes that mixes supernatural and horror Both series' stories are gets darker as the episodes progresses Melody of Oblivion and SoulTaker are two series that executes horror in a way that is seen as horror at a more realistic level. 

atleast the first half of Dragonaut will remind you of Melody. 1. they ride machines, that have a human form. 2. the riders have a special bond with machine 3. the protagonist's lover gets captured (first half of Dragonaut) 4. the lover is condemned to fate forced away from protagonist 5. they go in space 6. the lover has pink hair sorry for spoilers, and Dragonaut's machines are dragons not machines, i think, they kinda look like machines though 

it is mostly the feel of the story, especially the psychological part (even though NGE is more confusing than MoO) the story plot is similar in the sense that the good guys, Meros Warriors (MoO) and Evangelion (NGE), and the bad guys, Monsters (MoO) and Angels (NGE), battle what seemed to be a very long battle.. both endings are about the same where they are left hanging, and left for the viewers to imagine. 

both are anime that fight with music, yes very silly 

Main male is the loser at school, runs away with main female Main characters have a link with their mecha Main female "had a thing" (kinda a stretch in Eureka Seven) for the main males role model but then falls in love with main male The group travels alot Part of Rebelling group  

Both series feature a war being fought for humanity, Melody of Oblivion after the war is over, and Gunbuster as the war is being fought. Gunbuster has superior animation, characters, and story to Melody of Oblivion though. 

A story about a boy who travels with his Bike companion ( Elan Vital, a high tech bike *fighting Machine*), though it has a plot that follows through all the episodes. It is far from close but they do feel related. 

Same writer. Same Gainax. Same madness. :) Only MoO is longer and more slow-paced. 

Surrealism. Whether you've encountered a MM Witch or a MoO Monster, say good-bye to laws of physics and logic. 

I wanted to rec something that gets the dark fantasy, strange world, vibes /and/ the dark sexuality right, where I thought Gleipnir does a pretty poor job with the latter. Melody of Oblivion does not, still after I can't say how many shows watched one of the most strangely sensual anime I've seen. The shows are similar in that there is a hidden conflict going on in both worlds that only a select few are aware of and participating in. The manifestation of abilities covers a lot of ground in the monsters of both shows.  

Both of them have stories that are utterly baffling and yet profound and gripping.