Unlike the Bible which has a wealth of archaeological and manuscript evidence supporting it, the extravagant claims central to the Book of Mormon remain as unevidenced as any fairytale. No evidence has surfaced for an arrival of Jews to America, the existence of swords, chariots, or horses in America prior to Columbus, or that Native Americans are descended from Jews.
Mormonism openly disagrees with the Bible. In my case, I have met Mormon missionaries who initially pretended Mormonism acknowledged the Bible's authority, but afterwards discovered the Mormon church teaches that the Bible is flawed and the Book of Mormon is superior. This is an inevitable necessity for the LDS Church since there are numerous places where the Book of Mormon contradicts the Bible, including:
Mormonism teaches that dark skin is a curse from God, per the debunked Mark of Cain theology which was briefly popular in the 18th century when the Book of Mormon was created:
2 Nephi 5:20-25 Wherefore, the word of the Lord was fulfilled which he spake unto me, saying that: Inasmuch as they will not hearken unto thy words they shall be cut off from the presence of the Lord. And behold, they were cut off from his presence. And he had caused the cursing to come upon them, yea, even a sore cursing, because of their iniquity. For behold, they had hardened their hearts against him, that they had become like unto a flint; wherefore, as they were white, and exceedingly fair and delightsome, that they might not be enticing unto my people the Lord God did cause a skin of blackness to come upon them. And thus saith the Lord God: I will cause that they shall be loathsome unto thy people, save they shall repent of their iniquities. And cursed shall be the seed of him that mixeth with their seed; for they shall be cursed even with the same cursing. And the Lord spake it, and it was done. And because of their cursing which was upon them they did become an idle people, full of mischief and subtlety, and did seek in the wilderness for beasts of prey. And the Lord God said unto me: They shall be a scourge unto thy seed, to stir them up in remembrance of me; and inasmuch as they will not remember me, and hearken unto my words, they shall scourge them even unto destruction.
This of course is in direct contrast to the Bible which teaches that dark skin is simply a result of sun exposure and is not a basis for looking down on others. See Dawkins' Criticisms for greater detail about what the Bible teaches about skin color and racism:
Song 1:5-6 I am black, but comely, O ye daughters of Jerusalem, as the tents of Kedar, as the curtains of Solomon. Look not upon me, because I am black, because the sun hath looked upon me: my mother's children were angry with me; they made me the keeper of the vineyards; but mine own vineyard have I not kept.
Mormonism teaches that Jesus separately appeared to the Native Americans in human form to perform ministry, which aside from having no historical evidence directly contradicts the Bible.
3 Nephi 11:1,7-10 And now it came to pass that there were a great multitude gathered together, of the people of Nephi, round about the temple which was in the land Bountiful... And behold, the third time they did understand the voice which they heard; and it said unto them: Behold my Beloved Son, in whom I am well pleased, in whom I have glorified my name—hear ye him. And it came to pass, as they understood they cast their eyes up again towards heaven; and behold, they saw a Man descending out of heaven; and he was clothed in a white robe; and he came down and stood in the midst of them; and the eyes of the whole multitude were turned upon him, and they durst not open their mouths, even one to another, and wist not what it meant, for they thought it was an angel that had appeared unto them. And it came to pass that he stretched forth his hand and spake unto the people, saying: Behold, I am Jesus Christ, whom the prophets testified shall come into the world.
The Bible on the other says there will be only two comings of Jesus, not three, and that the second will be visible to the entire world. Jesus warned of false prophets like Joseph Smith who would claim Jesus was secretly appearing to a select group. Jesus said His coming would be open and obvious to the whole world, as easily seen as lightning which shines from one side of the sky to the other.
Matthew 24:23-30 Then if any man shall say unto you, Lo, here is Christ, or there; believe it not. For there shall arise false Christs, and false prophets, and shall shew great signs and wonders; insomuch that, if it were possible, they shall deceive the very elect. Behold, I have told you before. Wherefore if they shall say unto you, Behold, he is in the desert; go not forth: behold, he is in the secret chambers; believe it not. For as the lightning cometh out of the east, and shineth even unto the west; so shall also the coming of the Son of man be. For wheresoever the carcase is, there will the eagles be gathered together. Immediately after the tribulation of those days shall the sun be darkened, and the moon shall not give her light, and the stars shall fall from heaven, and the powers of the heavens shall be shaken: And then shall appear the sign of the Son of man in heaven: and then shall all the tribes of the earth mourn, and they shall see the Son of man coming in the clouds of heaven with power and great glory.