I have just done a short stretch, for the first time - and yes, there is something undoubtedly unique about the experience. The specifically spiritual aspect of the journey - whether one has faith or not, separates it from other hikes, other journeys sharing the road, accomodation and companionship with others. It gives us permission to explicitly incorporate in the journey a search for something within ourselves, and (if one wants) to share that with others.
That is not always the easiest thing to undertake in any other circumstance, and I am reminded of Steinbeck's 'Cannery Row' - when the character Doc, finds that if you don't want to raise suspicions when doing something outside of mainstream experience, then it is easiest to come up with a facile motive. He ends up telling people that he is walking across the country not from the wish to experience it intimately, but because he has been bet $100. Instead of suspicion and hostility, he is then greeted with help and goodwill.
Perhaps with the mainstream marketing of New Age spiritual quests, there is not such a sense of discomfort about such motives now (but I can't imagine anything more toe-curling than having my chakras fiddled with by some failed middle manager). But undoubtedly, the Camino is a perceived legitimate reason to shed the trappings of our lives, and to embark on a spiritual journey, as well as a demanding physical one. Combined with the experience itself, that is a very powerful draw.
Pip