Honestly, I think they're both awesome, but The Sword of Justice is a Tyrite weapon and should only be wielded by a Tyrite Cleric with Greatsword Proficiency (through Feat Pick at Level 4) or Paladin of Tyr. At the very least, it should be limited to being able to be used by someone who is affiliated with good, like a Cleric of Paladin of Selune, etc. Certainly, if you are a murder hobo going around killing people in the grove, you shouldn't be able to use it.
Likewise, Everburn is a sword of a Demon Commander. Probably shouldn't be able to use it unless you're an evil murder hobo.
I don't know if I agree with you so much on who SHOULD be able to wield the weapons... I agree thematically the Sword of Justice works really well for a cleric of Tyr (which I happen to be playing atm and have give great sword mastery to along with 3 other weapon types), but as far as Only good Character's being able to wield one and only Evil characters being able to wield the other... Eh, that really doesn't work for me, particularly in this game.
1) it is a rarity that a weapon is alignment locked... not saying it doesn't happen I have played a couple D&D campaigns where an alignment locked weapon was introduced, but all in all they are kind of rare and (in my experience) more often than not those weapons are intelligent or some sort of demon or deity speaks through them.
2) All the character's except for the player character are Morally Grey (you can be the purest angel of mercy or the a demonic murder hobo and anything in between) the "Evil" aligned characters kinda walk that line between neutral and evil and the "good" characters walk the line between neutral and good imho (and that is fine, I like flawed characters that don't fit neatly in to an alignment box, makes them more "human")
3) and this is my Biggest argument against this in BG3... BG3 seems to lack an alignment system... or at least a visible one.