Disclaimer: I don't know Japanese
I read both translations.
In terms of faithfulness, MangaPlex seems closer to the Japanese , though this isn't always good thing (cue skill name of "Breath flame", when it's coming from her hands. Though it's technically fine (if you change breath to breathe), Caliburn's "Breath of fire" just feels nicer). When it comes to the names, I prefer Caliburn (e.g. Lævateinn vs Reyvatein, where the latter seems more accurate based on lore and the title of the manga).
MangaPlex's typesetting (in specific, font size, though there's a bit of bold on Caliburn's that I feel hurts reading) feels easier to read. Besides that they're more or less the same in word choice, just different word orders (though MangaPlex's Page 12 3rd panel "Do I have amnesia" seems to be in the girl's speech bubble, which doesn't fit
@rspreet)
Not sure what the group's are going to do, though judging by the times of releases, it's probably just a coincidence, but translation and redrawing are pretty much the same.
Ty for the chapters!
EDIT: I said "latter" instead of "former" (as a typo) in regards to "Lævateinn vs Reyvatein" - however from chapter 2, it seems that the author intended for the name to be Reyvatein since the translator said the reason for using it was embedding it into a sword's guard, so it seems like the author intended that to be it's actual name.