What's the difference between:
- What a rude person you are!
- How rude you are!
- How rude of a person you are!
- How rude of you!
Which one is correct? Please give me some elaboration so I can understand, thanks.
So ultimately, these sentences are all equivalent, as P.E. Dant said in a comment above. However, there are some VERY slight nuances between some of your sentences, nuances that most people wouldn't actively acknowledge, but might color one's interpretation when hearing it.
What a rude person you are!
The use of "what" and "a person" here, makes this an assertion of holistic rudeness. In this case, you're saying that it isn't simply their actions that were rude, but their entire being is rude. This is severely harsh.
How rude you are! and How rude of you!
Using "how" and "are" or "of you" makes this more about their current action(s). It's less an assertion of poor character as above, and more an assessment of their behavior at the moment. This is less severe an indictment, and implies that they should fix their behavior.
How rude of a person you are!
Not grammatically correct (unless you remove "of").
EDIT: "What" is related to something's existence whereas "how" relates to what something does. This is the major difference that I attempted to outline above. I felt like this addition might make it clearer.
Luckily, the difference is quite easy to sort out.
What + noun phrase:
What a rude person (you are)!
What a beautiful day (this is)!
How + adjective or adverb:
How rude (you are)!
How beautiful (this is)!
How quickly they grow up!
Except for adverbs, these must be followed by an inverted verb + subject if you use a verb at all.
As @Rhythmatic wrote in his answer, you can certainly paraphrase using the other part of speech for a different feel. The following are functionally equivalent:
How obedient he is!
What an obedient child he is!