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Cost explanation: It's much less powerful than brilliant energy, for starters. It really only gives a boost against undead and constructs. Would you rather have this, or a +2 property like bane or holy? Almost certainly you'd want bane or holy, so this probably isn't a +2 property. Would you rather have this, or a bonus +1d6 damage from energy, or a property like ghost touch that lets you bypass the 50% miss chance for incorporeal undead? That's a hard one to decide ... different circumstances might make you choose any of the three. So, I'm pricing it at +1.
Update: Someone pointed out to me that this sort of weapon lets you hack through walls really easily, making walls and castles much less of an obstacle. With that in mind, it probably should be a +2, so I changed the price info in the stat block.