Adjective clauses are generally introduced by relative pronouns. The
relative pronouns are who, whom, whose, which, and that. They are
called relative because they relate the adjective clause to the word
that the clause modifies. Besides introducing the adjective clause, the relative pronoun has a function in the clause.--Warriner's. 127.
The relative pronoun can introduce the clause and be its subject, or act as a direct object, and so forth. However, there are times when the relative pronoun serves no other purpose in the dependent clause but to introduce it. Each adjective clause has a subject and a verb and adjective (called a predicate adjective).
I am more certain that he is healthy than that he is wealthy.
So, in this instance the relative pronoun that functions as a pronoun but serves no other purpose in the dependent clause but to introduce the clause; thus, it can be omitted, which is often the case. When left out of the sentence, it is understood. So both versions are correct.
John E. Warriner. Warriner’s English Grammar and Composition. Third Course. Liberty Edition. Orlando, Florida: Harcourt, Brace, and Jovanovich. 1986.