Let the Nazgul be LotR's thing, while TH will have a whole new tone and explore new aspects of the world. I expect we'll see all sorts of monstrosities in Dol Guldur, possibly Vampires, Werewolves, and Eru knows what else. It's the kind of environment which would appeal to both PJ and GdT's sensibilities, so I'm sure there's no lack of attention paid to the denizens of the Tower of Sorcery. What would really be cool is if Sauron has all manner of bizarre creatures in his dark tower, such as Wights, Zombies (he IS a Necromancer, after all), Lovecraftian horrors akin to the Watcher in the Water, ETC. Hopefully, the things in Dol Guldur will make the Nazgul look like silly pansies! [tongue]
However, IF the Witch-King is included, it would be a good chance to make the character even more detested by the audience...it would add an extra layer of resonance if in RotK when Eowyn ends the Witch-King's existence, it's not only comeuppance for attacking Frodo and Theoden, but for further evils the Nazgul committed in TH as well, (killing Tauriel)?
Also, it would give PJ a chance to redesign the Nazgul's armor/outer appearance, (making them fit in with Sauron's Mirkwood phase), which could potentially be fun as well.