Which one of the following is correct and why?
It'll be wonderful to see you again.
It'll be wonderful seeing you again.
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Both are correct. Either the gerund clause or the infinitive clause can act syntactically as a [NominalPhrase] in this construction.
The construction it + BE + [AdjectivalPhrase] + [NominalPhrase] is a rearrangement of the ordinary sentence [NominalPhrase] + BE + [AdjectivalPhrase] which focuses on the [AdjectivalPhrase].
To see you again'll be wonderful ... > ... It'll be wonderful to see you again.
Seeing you again'll be wonderful ... > ... It'll be wonderful seeing you again.
The pronoun it refers to the longish [NominalPhrase], and it's put at the head of the sentence so you can give the [AdjectivalPhrase] wonderful a more focal position, before [NominalPhrase] which is tacked on at the end to clarify what it is.
Note that when an ordinary noun phrase rather than a clause is employed as the [NominalPhrase], it must be separated from what goes before with a comma or dash:
Paris in the spring will be wonderful ... > ... It'll be wonderful, Paris in the spring.