It seems that there are three possbile foundations upon which religious belief can be founded: reason, spiritual experience, or a combination of the two.
By 'reason' I mean those things that are demonstrable, or are based upon credible scientific, historical, experiential, or philosophical foundations. I imagine one who gains belief through reason as an individual who, through observation and/ or study of credible sources, concludes that a certain religious world view offers the best explanation of the human condition. For example, an individual may become a Roman Catholic because the moral theology and ethical view presented by the faith seems to best explain morality and the world as he or she has experienced it (i.e. the solution to improving society's condition is to promote traditional marriage and family values). This seems to have been the case with converts such as Alasdair MacIntyre and Leah Libresco.
While I have encountered many that believe, at least in part, on the basis of reason, most with whom I have interacted base their faith primarily on subjecive sensory or emotive experiences. As one who has never had an experience that would compel me to belief, it is difficult to opine about this topic. Perhaps if I too experienced such feelings I would believe. That being said, there is an obvious problem with the subjective spiritual experience. If a Christian claims to know their faith is true because of a spiritual experience, and a Muslim claims that their faith is true for the same reason, and we have no higher standard by which to judge the validity of a faith, neither can make claim over the other. In assessing the opposing religious truth claims of two parties there exist only two logical possibilities: one is right over the other, or both are wrong. If a person of faith wishes to argue the truth of their faith over others, they must base this claim on evidences available to third parties.
There are some who claim that whether or not their faith is true isn't important. Such is the basis of the modern, relativistic claim that "what is true for you isn't true for me." I would wager that most religious and spiritual people, if pressed, do not actually believe this idea. If I claim that my Buddhism is true for me, but your Islam that claims to be the only truth is also true, I am speaking an obvious contradiction. What people likely mean when they say "my truth isn't your truth" is "one of us is indeed right, and the other is indeed wrong, but what difference does it make?"
This is a good question. Why should one be concerned with truth? There are obvious cases where it is important to know the correct option due to consequences (Is it better to play dead or run if you encounter a bear?), but then there are truths that are of no consequence. (How many galaxies are there in the universe? Did the apostle Paul have a beard or not?) I may take up this question in more detail later, but for now I will simply state that it seems obvious that one's religious beliefs can have a profound effect on how they view and live life, and thus we cannot pretend that all faith traditions are equally valid.
While I recognize the importance of spiritual/ mystical experiences, I maintain a firm conviction that faith should not be based primarily in the subjective experience, especially if one wishes to make public claims to being the fullness of truth over other faith traditions. From here on out the claims of both the LDS and Catholic faiths will be assessed through this lens.