Masamune, caladbolg as well.
Was about to say!
Concerning the three empys in the list here's my take:
Kannagi
It's a weak Katana for NIN, comes behind most other options in most situations.
Main reason for this is that Blade: Hi is atm a bad WS with bad scaling and a bad mod (AGI).
The main pro of Kannagi R15 is the white damage, and as such is shines only in content where that's relevant.
Only example that comes to mind is the Qutrub Ambuscade.
I personally have one but I basically never use it.
Rhongomiant
I'm not a big expert of DRG but I think this is a bad option surpassed by many other. Even the Ambu one is better than this when it comes to damage.
Gandiva
This is an interesting option.
It's probably the weapon with the highest DPS potential, despite the odd mod (DEX).
Main problem with Gandiva is actually getting hate too early. When that's not a problem Gandiva shines.
tl;dr
between the three weapons listed I'd say Gandiva is the one with the highest utility potential for its respective job.