They can both be synonyms in certain situations. "Benar" has a stronger association to mean what is appropriate or what is just. "Betul" is usually just associated to what is right or wrong, true or false, correct or incorrect, authentic or artificial. So "benar" is more relative and open to interpretation while "betul" is more straightforward and Boolean.
The english sentence is awkward again. If contrasting opposites in English, the matching words needs to be used. For example, you would contrast correct with incorrect, accurate with inaccurate, and wrong with right. In this case, you would say, "The book is right and you are wrong." Is that not the case in Indonesian?