Whew. I've never commented before but I feel like I can clarify a few things. (Honestly, I just feel more comfortable on Discord than comment sections)
Here we Gooooooo~
Both mangas started at roughly the same time, so there is no "who came first" issue really. They both came together.
This manga (henceforth referred to as GX) is an entire half a novel volume worth of story ahead of the other one (BG).
The main difference between them is TONE and the audience. I shall explain.
GX is targeting an older audience. If you check the RAWs, comparing to BG that has ruby/furigana for every. single. damned. kanji. GX's ruby usage is more in line with the novel's.
BG is more of a comedy. Lots of dynamic panelling and expressive faces.
If that is the reason you like BG, you will not like this version.
GX is more of a drama. Lots of quiet moments, Jinshi blushes (a lot) and you get a more grounded version of the story.
If the reason you liked the other manga was the characters and story/romance, you will like this one.
All in all, they are 2 completely different tellings and if you're a fan of this franchise, you should read both.
[EDIT] Oh and BG skipped an ENTIRE MYSTERY and some character development... so there's that. LOL