I don't see how it is in any way possible to establish one or the other, or any parameters of the question. Faith in what? If in "God" of any sort, there is no empirical way of proving or disproving that such a being exists; there is no possible experimental model. If in human nature, well, you can have faith that human nature is complex, that some people are sometimes more "good" than "bad" and sometimes the opposite, but history bears out little else. "Luck" is also a concept whose existence is impossible to establish in any way.
Any specific example given of a person or persons surviving or failing to survive would be subject to interpretation of faith, luck, or just coincidence or "that's the way it went." Frankly, this is a question that has no real meaning. The only impact of these concepts would be in the mind of an individual, one might believe oneself the recipient of faith or luck, but there could be no empirical proof of either one.