The bottom line authority is what makes it different - such authority which can not be seen per se but is believed.
Muslims believe that Allah sent an angel to dictate to Mohammad the words of the Quran. They then believe Mohammad (who was illiterate) verbally shared these with his followers who later wrote them down (just as Mohammad wrote, they believe).
Mormons believe that Joseph Smith translated golden plates out of ancient Egyptian hyroglyphics (in spite of the fact that linguists disputed the idea), and gave them "the other Testament of Jesus Christ." They also believe in the inspiration of the Pearl of Great Price. In short, they trust their prophet.
Other holy books are written down by the holy men of those religions, though they don't necessarily believe in a personal God who would have inspired them.
Christianity makes certain truth claims about its Scripture (which Judaism echos). That is God inspired men of God what to write in the Word of God. This inspiration encompassed 40 some writers in over 60 books over 2000 years time and is unified in message, content, and purpose. Our authority to believe the Word of God is not a prophet who told us so, but it rests in the inspiration of God Himself. It is an intangible though. The Holy Spirit bears witness to our spirit. We can look at reality and see how well God's word matches up to it. We can see how well it reflects history. But, ultimately it is faith in the God who inspired it. Thus, our faith rests in God because Scripture says it was inspired by Him.
If Scripture is the mere writing of men without being fully inspired by God, it has less of a foundation for belief than many of the other religions. Frankly, it is untrustworthy.
I'm sorry, I still don't see the distinction. Muslims and Mormons have faith in "the God who inspired" their scriptures also.
Maybe this part is of your reply provides more of a way:
We can look at reality and see how well God's word matches up to it...
How so?