Dementor Vs Ringwraith

There are many parallels between Harry Potter and Lord of the Rings characters, such as giant spiders, old white bearded wizards, giant trolls and I'm sure many more. I'm also sure you can connect both of these to other films/books/whatevers too, but one of the the biggest that stood out to me was the similarities between the Nazgûl from Lord of the Rings and Harry Potter's Dementors. They do have their own origins, abilities and motivation, but personally I always found them fairly similar in appearance and the way they both track down the protagonists. I just wondered what would happen if these two were up against each other. Who do you think might win in such a fight?