I've been comparing the closing credits from Platinum and the new blu-ray (specifically for episodes 25 and 26), and noticed a number of differences. Do we know which is more correct?

The DVD has #26 script - Hideaki Anno, Masayuki, Kazuya Tsurumaki; Storyboards - Masayuki
The blu-ray has #26 script - Hideaki Anno; Storyboards - Masayuki, Kazuya Tsurumaki, Hideaki Anno

The DVD has Production Coordinators Takahiko Sakagami, Yuh Kiyozono for both episodes, while the blu-ray has Production Assistants Takahiko Sakagami, Yu Jyoen for #25, Manabu Ishikawa, Masao Yoshida for #26. Is Production Coordinator and Production Assistant the same thing?

DVD has Chief Animator - Takeshi Honda, Animation Director - Yasuto Murata, while blu-ray has Animation Director - Takeshi Honda, In-between Animation Check - Yasuhito Murata.

Production in Cooperation with Vega Entertainment and #25 Finishing - Mizo Planning seem to be missing from the blu-ray credits.

There are a lot of names that differ to a greater or lesser extent. Typos? Alternative but equally valid romanizations? Nicknames vs formal names? Updated to reflect changes to the person's actual name since the DVD?
Tetsuo Iwanaga / Tetsuya Iwanaga
Yudo Oishi / Hiromichi Oishi
Yuh Kiyozono / Yu Jyoen
Naoya Furukawa / Hisaki Furukawa
Sadafumi Hiramatsu / Tadashi Hiramatsu
Yasuto Murata / Yasuhito Murata
Hidero Kawabata / Hideo Kawabata
Hiderou Isa / Hideaki Isa
Eiko Kitazume / Hideko Kitazume
Harumi Takahoshi / Harumi Takaboshi
Atsushi Wakemiya / Atsuki Bekku
Chieko Odaka / Chieko Kodaka
Naohisa Atsushima / Naohisa Haijima
Yuhichi Ono / Yuichi Ono
Taketo Koyasu / Takehito Koyasu
You Yoshinari / Yoh Yoshinari
Takaomi Kanezaki / Takaomi Kanasaki
Ayako Shibata / Fumiko Shibata
Hiroshi Ohta / Masaru Ohta
Masako Sato / Masaru Sato
Yasuchika Kondo / Yasuhiro Kondo
Korato Yokoyama / Koutaro Yokoyama
Aiko Arai / Maiko Arai
Hijiri Kouhara / Hijiri Kamihara
Sound Team Donfan / Sound Team Don Juan
Souiji Shiihara / Soushi Shiihara
Shirou Sagisu / Shiro Sagisu
Toshiyuki Ohmori / Toshiyuki Omori

The 2003 renewal credits appear to apply to the entire series, not specific episodes. Was any renewal work done on 25 and 26, or was did End of Evangelion replace them?

To answer your final question, that's correct. Episodes 25 and 26 don't have the "Director's Cut" versions that came for the previous four episodes of Renewal (21' to 24').

About the closing credits, those are very good questions. Knowing of ADV's reputation, it's likely that Platinum is the inaccurate one. Unless confirmed otherwise, go for the Blu-Ray.

With the names listed, a number of the names in the Platinum set are wrong due to errors in ADV's transcription. Japanese names are often written in the Kanji characters, and there are multiple ways that a Kanji can be read, and it is a sign of sloppiness that these names have been transcribed wrongly. The most glaring errors are with Tetsuya Iwanaga and Takehito Koyasu's names, since both of them are well-known voice actors whose correct names are easy to look up. Some of the other changes in spelling are due to use of different Romanization systems. "Shirou" and "Ohmori" are different spellings of "Shiro" and "Omori" intended to indicate a long "O" sound, but it appears that the latter spellings are the preferred ones.

As is the case with the credits, the names and spellings used in the Blu Ray are the correct ones unless confirmed otherwise.

Thanks! I knew Kanji could have multiple meanings, but didn't realise they had multiple pronunciations as well.

As I understand it, Renewal also has a lot of new background dialogue in episodes 1-20, as well as the four extended Director's Cut episodes. I'm guessing there's no such new dialogue in 25 and 26? Though they do have new 5.1 audio.

Episodes 25 and 26 were two episodes that never needed any additional background dialogue because they turn to examining the psyches of the characters. The vast majority of the added background dialogue consists of chatter among scientists and operators, announcements and other things in Nerv HQ, with maybe some more lines added in classroom or Tokyo-3 scenes. The last time Nerv HQ was involved in the TV series was when Kaworu took over Eva-02 and headed to Lilith's chamber.

The wikipedia article on different readings for Kanji covers the subject pretty well. With personal names, there may be "mixed readings" and local variations that cause further confusion, especially for the less common names.
https://en.wikipedia.org/wiki/Kanji#Readings

That's not even getting into the subject of Japanese romanization, which can cause significant additional confusion to those unfamiliar with it.
https://en.wikipedia.org/wiki/Romanizat ... rn_systems

For the English credits, Platinum DVD, episodes 25 and 26, is it correct that the cast credits should be:

Gendo: John Swasey
Shigeru Aoba: Vic Mignogna
Maya Ibuki: Monica Rial

And not Tristan MacAvery, Jason C. Lee, and Kendra Benham? Was all their dialogue replaced?

It's odd that they didn't update the cast credits at the time, since they did add the Renewal credits.