I've been messing with the mnk dps calculator to check on this as it doesn't seem like a point of interest to most monks/puppetmasters, but I'm not the best with excel so take this with a hefty grain of salt. It seems as though the weapons are reliant on applying defense down in order to be competitive. Without def down, they seem to be slightly worse than it's competitors, but after applying defense down, they pull slightly ahead. Thankfully the proc rate is quite high, at least on the hq. To check the effect of defense down, I recorded the overall dps value with and without def down applied. Hopefully a real mathematician can accurately determine how they compare to other h2h options if you were looking for a more detailed answer.
On the plus side, the nq only costs ~3M, which is about the same cost of the geodes and avatarites for the fire h2h without the horrible grinding or you can attempt to farm the meeble claws to save gil. Also, they may be of some use even if you own a R/M/E h2h as I've tried the humorous advice of a friend to apply the def down first, then switch to something else to get the best of both weapons. I only own the WoE+2 h2h to switch to, but smite still beats shijin easily in abyssea and I still retain the def down effect for the next 3 minutes after switching. At the very least, other DDs will love you for helping increase their damage output.
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