Asking what is held in higher regard the Bible or Book of Mormon, is like asking a person what do you hold in higher regard the food that nourishes you or the air that sustains your life.  
 
Without both books Latter-day Saints are lost, we need the entire Gospel of Christ not just parts of it to guide us and teach us the will of our Heavenly Father.  
 
We accept the Bible as far as it is translated correctly (which we hold the King James Bible to be correctly translated) and the Book of Mormon complements the Bible adding strength to the teachings of the Bible and adding a second witness of the Commandments of Christ.  
 
A good way to explain how the Bible and Book of Mormon work together is the following anecdote. If you take a singe point you can put an infinite amount of lines through it, this is like the Bible and the limitless number of interpretations the various sects of Christianity make of the Bible.  
 
With only one point of reference there no limit to the way the message can be twisted or interpreted to mean the exact opposite of what is said.  
 
Now if you add a second point of reference, there is only one line that can be drawn between the two points, only one interpretation.  
 
This is what the Book of Mormon does, it adds a second reference point to clarify and remove the man made interpretations and doctrine that polluted Christianity in the time of the Great Apostasy.  
 
The Book of Mormon was brought forth by Heavenly Father to confound the revilers of this Church the one true Church of Christ, and restore the plain and precious truths of the Gospel of Christ lost due to the cunning work of men.  
 
In my intensive study of the Bible and the Book of Mormon I have found no contradictions, unless they were caused by grammatical accidents in the writing of the scribes thousands of years ago.  
 
There will not be contradictions between the Book of Mormon and the Bible because they are both inspired by the Holy Ghost and contain the Word of God

Thank you for your response! I recently went to a Mormon meeting, and one of the teens explained to me the "circle method." That makes sense and it will really help prevent needless stalemates went talking with my Mormon friends. 
 
But as for contradictions, there are a few I have found (I hope you haven't seen these too often, I don't want to bore you).  
 
This verse is from the King James Bible- John 3:16- "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life." This verse is contratictory with the belief that Lucifer/Satan is also God's son. 
 
There are also several verses that state the Christ is God, so here is a verse from Kings James Bible, John 1:1-3 "In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made." 
 
There are 3 things that can be taken from this that contridict Mormon belief: First, that Jesus is not only with God, he IS God. Second, that Jesus was with God in the beggining, so He couldn't come after God. Lastly, that Jesus made everything, which included Lucifer, because nothing existed before Jesus and God.

The only contradiction I saw was in your explanation, you say that Lucifer is not a creation of Heavenly Father through Christ, then in your next statement you say that he was created by Heavenly Father through Jesus Christ.  
 
Which one is it? 
 
Is Lucifer a creation of Heavenly Father's of not? If he is he is a Spirit Child of Heavenly Father. Not yes he did rebel but that did does not mean that Heavenly Father does not love him any less. Lucifer and his angels DO believe in Christ every time they meet him in the New Testament they call him by his holy name, the Son of God.  
 
The reason why Lucifer is beyond salvation is he openly rebelled against Heavenly Father and denied the Holy Ghost which is an Unpardonable Sin, so Lucifer is not able to be saved through John 3:16 
 
Also John 1:1-3 does not contradict any of the doctrine of the Church of Jesus Christ of Latter-day Saints, in fact it is a verse that supports our 8th Article of Faith. That we accept the Bible as the word of God as far as it is correctly translated.  
 
The most accurate translation from the Greek and Hebrew into english is "he was a God" not "he was God". The passage makes no sense in the context you take it as, how can someone be with someone and be that person also.  
 
The problem is that the Greek does not cleanly translate into English. Pathos the greek word used, can be interpreted as a person (God the Father), a descriptive noun (a God, as I hold to be the most correct), it can also refer to a state of being or nature (referring to Christ's Godhood or Divine Character inherited from his Heavenly Father).  
 
This is the problem with translation, to know what Paul is saying you have to take the translation in context of his teachings. Paul does not teach a triene Godhead, he teaches like Christ and all the Apostles do that the Father, Son, and Holy Ghost are three exalted personages who are untied in purpose as the Godhead.  
 
As I previously said before there is no contradictions between the Bible and the Book of Mormon. Both are inspired scriptures sent by the power of God through the Holy Ghost to his Prophets.  
 
This same poor argument is used by Anti-Christ around the world against "mainstream" Christianity. That the Old Testament contradicts the New Testament. Which is also false, taking the scriptures out of context does not make them contradict each other.  
 
I hope my answer clears up some of the confusion

Please look past my typo when I put Paul instead of John, I have no clue why I put Paul instead of John as the author of the Gospel of John. My apologies for that typo!

You say on this site, quote : " We accept the bible as far as it is translated correctly (which we hold the King James Bible tp be correctly translated. Joseph Smith said the King James Bible was faulty and that god had instructed him to write the Inspired version of the Bible. So why don't you use that version ?