You should use the one that you find more convenient to keep updated. On a different distro I would say use the utility, but with rolling release I’m updating my system constantly anyway so I don’t find these Wine/Proton management applications to be all that useful.
As for the day-off version discrepancy, I’d imagine that would be ironed out quickly if it were to occur.
The pacman one is also v3 yes. With that one it’d just be noted in the repository it came from instead of the package name.
Also is that a copy+paste of the protonup package name? Or did you type it out manually? The sIr instead of slr is troubling?
If you download the version that supports your CPU extensions I do not believe there should be any practical difference apart from convience of it being updated as a system package.