Christians who believe in the NT hold to the belief in a Triune God, One God in Three Persons. The Trinity maintains monotheism and is consistent with such a belief. The One God YHWH of the TANAKH is who they believe in.
Muslims hold to Unitarianism and reject the Trinity outright, although the Quran has no idea what the Trinity actually is, as found in Surah 5:73-75 and Surah 5:116. Allah himself is not YHWH, but is a god of Muhammad's own imagination masquerading as YHWH.
Mormons hold to a form of henotheism or polytheism, though the Mormons will take offense at such terms. Regardless, They believe that YHWH is Jesus and Elohim refers to the Father and believe they are two Gods. This is inconsistent with the biblical witness of the scriptures. Though the Mormons claim to believe in the God of the Bible, they do not.
View of the Scriptures
Christians hold to the TANAKH as the infallible word of God with no errors and contradictions. Even in the NT it is recorded that the Bereans studied the TANAKH diligently to see if what Paul said was true. The TANAKH is regarded by the NT as the God breathed scripture.
Muslims believe that the Torah and the Gospel have been corrupted or tampered with by the Jews and the Christians and thus believe the Quran came to restore the true religion of Abraham and correct the errors. Sam Shamoun has postulated that the Quran actually teaches that the TANAKH and the NT are uncorrupted, but this won't be covered here. Regardless, Unlike Christians, The Muslims do not hold the TANAKH or NT as inspired, but see them as corrupted.
Mormons believe the Bible is the Word of God as far as it is translated correctly. While not as serious as Muslims, this is nevertheless a concern.
"You cannot find your leader just as they can't find their's"
Christians actually do try to look at the context to see if Jesus is found in the scriptures.
Muslims, while they claim Muhammad is in the Bible due to their Quran, some rely on absurd arguments such as Song of Solomon 5:16 on the basis of the word Machmmadim which means holy desirable or come up with absurd similarities to Moses and Muhammad in Deuteronomy 18. Muslims try to appeal to what they see as a corrupt source to prove Muhammad, which is inconsistent.
While some Christians may cling to Jesus due to an emotional tether, this isn't always the case and usually come to faith in Jesus by diligent study. Christians do encourage praying and studying the issues before coming to their own conclusions.
Muslims hold to a belief in Jesus simply because their Quran says so. Which makes me wonder why they like to use counter missionary arguments that would refute them.
Mormons will tell people to "pray to see if the Mormon church is true", based of a misreading on James 1:5, which actually talks about praying for wisdom and understanding.
I am aware there are so called Christians who are anti semitics, but the NT houses no such thing at all.
The other groups I have no comment at this time.
It is very clear that the comparing of Christians to Mormons and Muslims is not an argument that actually holds weight. I could highlight supposed similarities between Rabbinic Jews and Roman Catholics, but I could also highlight massive differences between these groups.
If Rabbinic Jews want to compare Christians to Mormons or Muslims in terms of tactics, I could easily point to the Roman Catholics and say they are like the Rabbinic communities. Either be consistent in the argument, or drop it.
Addendum: Additions maybe made should they come to my attention and this article may have extra info added. Also feel free to check out this article here: http://answering-judaism.blogspot.co.uk/2014/02/brief-comments-on-mormon-website.html