Compilation of Gendo's two endings from the PS2 version of Neon Genesis Evangelion 2.
Recording, editing, translation, and subtitles by Reichu (yours truly).
What constitutes a "Bad Ending" versus a "Good Ending" is mostly a matter of gameplay mechanics. Gendo, as the player character, needs to have a sufficiently high relationship with Rei in order to achieve the Good Ending. If this criterion is not met, then Rei will reject Gendo and instead hand the reins to whichever character she has the best relationship with instead. (And it can be anyone, not just Shinji, which is why Rei simply says aloud "Yonde iru", or literally "[Someone] is calling [me]", rather than specifying WHO is calling her.)
The Bad Ending has an outcome similar to the one shown in EoE, wherein Gendo is rejected but still visited by Yui so he can meditate upon his flaws. There are some crucial differences, which I won't give away. The Good Ending is effectively what would've happened if Rei had NOT rejected Gendo. I find it somewhat bittersweet, as my takeaway is that Gendo wants to forever exist in an idyllic past, which may never have existed (depending on what Rei's mysterious presence at the end means), frozen in time. It is open to interpretation, though, so please provide your thoughts below!
Translation is rather iffy in parts, since Gendo likes to speak in cryptic half-sentences.