I wanted to know the difference. Is it the nuance?
Could someone explain it to me?
Thanks in advance! :]
Simply なんと～(こと)でしょう is politer because でしょう is the polite form of だろう. It would be used when the speaker is talking politely, i.e., using ～です/～ます. Folk tales for children are usually narrated in this tone.
なんと～(こと)だろう is the non-polite equivalent, which is typically found in modern novels targeted at adults.
なんと～(こと)か is roughly the same as なんと～(こと)だろう, but it sounds a bit more literary and stiff. I don't think it's archaic. More examples here.
Neither is used in real life. Only in stories, anime, theatre, etc.
なんと醜い声であることか -- may be for an older reader. 19C classic for teenagers or adults. Heike or Konjaku translated into modern Jp.
なんと醜い声でしょう -- may be for a younger reader. Under 10. [Snow White]
The former sounds more male. More formal.
これはなんて美しい花なんでしょう！」 --- This sounds more like translated from a Western language. Grimm's tales, Le Petit Prince, etc.
ことか is used to express strong surprise.
でしょう is the polite form of だろう and is used to express probability.
How terrrible my voice is!
My voice seems terrible, doesn't it?