I have found a fresh way to look at multimedia.
This post is me ranting around Neon Genesis Evangelion, because that's how I came to the discovery, but these are not the point at all.
It's fun to see why, in terms of raw human experience, Eva (TV) got popular and inspiring for many, and how it could be possible to make what would have a more potent form of the impression it gives. I'm not viewing it as some model anime whose recipe must be followed to the T for any concept or premise as if that's the best way for anything. It's also helpful to observe the commonalities between other works, so it's possible to understand them better.

What features make a work of fiction an "Evangelion-like"? The lucid importance of each can be talked about for as much as it can be guessed intuitively, and being concise is possible.

IMPORTANT
I.1 Large mechanized units are the working horses of the main cast, additionally serving as little as a third point in a contrast network that also involves at least the main cast and the "outside" world.
I.2 The focus of the sentiment is on Mono no Aware. It's okay if the work does not abide by Mono no Aware in a traditional manner.
I.3 The work is at least light sekai-kei: it's only the consistent focus on a relationship between just two specific people that is optional. The main point is in the disproportionate, reality-warping relevance of relationships between the key cast.
I.4 The work has a welcoming mythological quality to it; it shouldn't merely count as an origin of a myth for any sequel — it should continue from at least a borrowed myth, if not the one it had handcrafted for the plot.
I.5 At least some of the main cast could be said to be common sense sensibility people put into a myth. Note that relatability without shared sensibility is possible.

OPTIONAL AMPLIFIERS FOR QUALITY
O.1 A kuudere character is featured within the main cast. Emotional detachment in face of I.4 amplifies I.2, I.3, and I.5.
O.2 At least the main character is young, because the lively youth is more relatable. Helps to amplify I.1, I.2, I.3, and I.5.
O.3 Uncanny and surreal subjects, imagery, and designs amplify I.1, I.2, I.4, and I.5.
O.4 Exposure involves multiple layers and sublayers of the world around the main cast. Amplifies I.3.

So, What Would (Not) Count?
For example, if you have only I.2, I.3, and I.5, you'd get Madoka (TV). You think you'd get an Eva-like if you put mecha in there, but Madoka (TV) does not really satisfy I.4. The Rebellion movie satisfies I.4 thanks to the prequel works filling in the mythos, but it handles I.2 in a warped way, yet, still, I think conversion to an Eva-like just by introduction of I.1 is entirely possible. Magia Record could easily become an Eva-like with just introduction of I.1.
Granbelm — "Madoka with mecha" — isn't mythological enough for I.4, despite there being contrast within I.5.
VOTOMS (TV) could feel like an Eva-like, but it has no I.4. It's rather anti-mythological.
New Getter Robo is the Getter installment closest to Eva, but its relatively prominent I.2 is not enough to count, and the main cast is, as usual, too deranged for I.5.
MegaMan Zero is a case that's interesting to me as it seems to be a close fit, but it would not count even if the main action was around piloting mecha. MegaMan Zero is too mythological. Even if Zero was being a detached half-amnesiac, it's too lacking in I.5, and whatever bond between Zero and X or Zero and Ciel there was, it didn't fulfill the core principles of I.3, as the archetypal mythology had overwhelmed them.
It's trickier to say why Muv-Luv Alternative, the best contender from Muv-Luv, doesn't fit. It's too subtle and restrained in mythology for I.4, and I.3 is too subverted to count.
Xenogears and Xenoblade Chronicles X are too lacking in I.2. The latter is straight up anti-I.3, and, somehow, the characters feel like archetypes rather than characters, so a proper I.5 is out of question for it, too.

What's funny is that, because of losing the grip on I.4, Eva Rebuilds feel less Eva than model examples like RahXephon or Gasaraki, as the Rebuilds had artificially and disproportionately invested into the unwelcoming anti-exposure narration that's typical of late/post-Gainax — it is the media equivalent of uncooperativity of an insecure schizoid man that's keeping all to himself because he's afraid of rejection. A catastrophically ironic failure to balance within the "hedgehog's dilemma."
Another peculiarity to bring up is that, just like Gundam works by Tomino (his I.4-lacking CCA would be the closest), the Armored Core installments in total have all of the features, but none has all of the features at the same time. AC6 is the closest, and is a polar opposite to Frame Gride that's just as close, but unconventionally. AC6 lacks I.2 and I.4 which Frame Gride got by trading I.3 and I.5 by having virtually no characters.