Okay, so here's the deal with "Elite". (Rant incoming, sorry.)
The first instance of this in Japan was Robotics;Notes Elite, which was a remaster of Robotics;Notes with improved 3D models/animations, slightly improved pacing, as well as adding a few cutscenes from the anime for some of the more action-packed parts. Actually a nice upgrade, all things considered.
At some point the company decided "Elite means anime! Fully animated visual novels are the future!" and made Steins;Gate Elite which replaced all of the graphics with scenes from the anime, and also created some new animation for the branching endings.
A lot of people already didn't like this idea because the original art style was so unique, but the real problem is that they didn't preserve the original novel in its entirety. Entire scenes and half of an entire chapter were cut because they didn't want to bother creating animation for them. Lots and lots of narration was cut (sometimes this is fine because it's just describing what you now see onscreen, but other times it seriously hurts the story and characterization).
The English localization suffers because the updated lines were retranslated by a different team than the original, introducing inconsistencies where the context in the Japanese lines doesn't flow properly from one line to the next, or the same line is repeated twice with a slightly different translation. Many typos were introduced as well, some of which really take you out of the moment.
They didn't make any script updates that would require recording new voice acting, which makes some lines fit oddly and none of the new jokes from the anime (which I found to have more variety than the VN) were included.
They greatly expanded the online message board sections, which on the one hand is nice for more authentic online interactions, but on the other hand really hurts the pacing of the early parts of the story and makes it harder to filter the important information.
The cell phone gameplay mechanic was butchered and minimalized, turning a lot of choices that used to be as simple as "answer your phone or don't" to "did you answer X number of texts from this character before now? cool, you're answering the phone whether you like it or not". You can't look at your text history and receiving attachments with texts was completely removed, even though some texts explicitly refer to included attachments.
The main reason to buy Steins;Gate Elite, as others have said, is for the bundled spin-off game which was otherwise never released in English.
I'm very worried about what they'll do for Steins;Gate 0 Elite, because if they don't change some of their process it's going to end up even worse.
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