>>1985
I wish I have that FAQ image up, but I guess I'll type them how I remember it.
>Rebirth;1 (Superdimension)
It's a remake done to make the original PS3 game's ending obsolete (ie. Where they give up their CPU powers to eradicate all the monsters.)
It was made to bridge the gap between the first and second game, but this game happens in it's own dimension where it's non-canon.
As a side note, this game's assets were taken from Victory (the third PS3 game in the series), which I'll explain later.
This game's localization is regarded to have the best one, but having a story in accordance with fan-fiction.
>Rebirth;2 (Hyperdimension)
A remake of the sequel (mk2) where it happens on the canon dimension, and where most character development happens.
It is mostly implied that the characters settled their war disputes just like in the first game, but not in the exact same way it did.
This game's localization is deemed to be horrible to it's material, but the story finally hits off in terms of an actual setting.
The /nep/ board was, and is hard at work in delivering the re-translation project to remove the memes and restore several dialogue that was originally replaced.
>Rebirth;3 (Ultradimension)
The third remake where dimension hopping became a common thing, while keeping the same canon characters from the 2nd game.
As a side note, this game will suffer more than the first two, because Felistella (The people who did the Vita port) re-used most of the assets from Victory (This game's origin).
And with no option in hand, they then again re-used the same assets from Victory for the third remake.
In terms of localization, this is the worst one yet.
Several scenes and dialogue were taken with impunity, where the original material is cast away in favor of meme humor.
The /nep/ board has their eyes set on re-translating this now that they're done with Rebirth;2.
>The Anime (Hyperdimension / Ultradimension)
A very condensed version of the last 2 remakes.
Episodes 1-5 are focused on the second game, where episode 6-12 are separated into two major story parts.
(Episode 6-10 are focused on the 2 newly added characters, and 11-12 are HEAVILY condensed for the "Perpetrator from the Past".)
The OVA is an extra to make the anime's ending a little more sweet, but unneeded.
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So to answer your question, it would be recommended watch the anime when you finish the games.
Or watch it while you're playing it, whatever works for you.