One important difference is that, in relative clauses in which the relative pronoun functions as the object of a preposition (you have just finished reading such a relative clause), "which" can be placed after the preposition, but "that" cannot:
She wrote a relative clause in which the relative pronoun functioned as the object of a preposition.
*She wrote a relative clause in that the relative pronoun functioned as the object of a preposition.
Another important difference is that, in nonrestrictive relative clauses, which are set of by a comma (like the one you have just finished reading), "that" cannot be used instead of "which":
She wrote a nonrestrictive relative clause, which needed to be set off by a comma.
*She wrote a nonrestrictive relative clause, that needed to be set off by a comma.
I have noticed that the second restriction seems not to have existed in the 1600s and earlier. Exceptions are plentiful in the King James Bible. In modern English, however, we cannot introduce a nonrestrictive relative clause with "that."