I have read multiple books on the Shikoku 88 Temples Pilgrimage and the Pacific Crest Trail. I have also walked short sections of both, and talked with people who were trying to complete one or the other.
Obviously, there are a lot of differences. The Shikoku 88 Temples Pilgrimage tends to go through settled areas, whereas the Pacific Crest Trail tends to go through wilderness. Most people who do the temples pilgrimage have a roof over their heads most nights, whereas most people who do the Pacific Crest Trail for any length of time camp outside most nights. The temples pilgrimage is about 1,100 km (670 mi.) long whereas the Pacific Crest Trail is about 4,250 km (2650 mi.) long. The temples pilgrimage was created for religious reasons by grassroots level religious devotees, whereas the Pacific Crest Trail was created by the U.S. government because a group of dedicated citizens advocated for it.
However, for all of the differences, there are a lot of striking similarities, or at least parallels.
Both have their own associated culture and lore. For example, the Pacific Crest Trail has the tradition of ‘trail names’ – nicknames assigned to hikers by other people (supposedly, one is not supposed to pick one’s own trail name). The temples pilgrimage has many of its own traditions, such as the tradition of getting a stamp from every temple. Some of these traditions are very similar – for example, the Shikoku practice of settai (giving things to the pilgrims) is very similar to the Pacific Crest Trail practice of ‘trail magic’ (giving things to hikers – this tradition also lives on the Appalachian Trail and other long-distance trails in the United States).
Both have spawned memoirs of the loser woman who is a personal mess and totally unprepared for the long trek, yet they do it anyway and discover themselves. I am, of course, referring to the bestseller Wild by Cheryl Strayed about the Pacific Crest Trail, but also Neon Pilgrim by Lisa Dempster about the temples pilgrimage.
Furthermore, both are treated as national trails – an experience which represents Japan / the United States. The Pacific Crest Trail is officially a National Scenic Trail. A lot of people attempt to complete the trails as a means of better connecting to their country. And these two routes do, in some way, represent the mythos of their respective nations. The temples pilgrimage represents a link with Japan’s cultural and historical past, in a region of Japan which supposedly has changed less over the past two centuries than the heavily populated metropolitan areas where most Japanese people live. The Pacific Crest Trail represents making forays into the ‘wilderness’, a pageant replaying the mythos of the United States of being a frontier nation where white people explore and settle areas which white people haven’t explored and settled before (yes, that is a colonialist view, but I am not going to unpack it right here). In short, I think it says something about Japan’s self-image that its great walk is centered on 500+ year old temples, and it says something about the United States’ self-image that all of it’s great walks, including the Pacific Crest Trail, center on great mountain ranges.
And though the Pacific Crest Trail is secular in nature, some people do use it for spiritual purposes, just as the temples pilgrimage is used for religious and/or spiritual purposes (I also would be unsurprised if people use the Pacific Crest Trail for religious purposes, but I do not have evidence of that).
I think the greatest thing in common between these two great walks is that many people use them to escape from ‘modern’ life. A lot of people who attempt both feel adrift – the ‘ordinary’ life of going to work every day is unfulfilling, or otherwise feel like their life is lacking in meaning – and they try to find this meaning by walking/hiking these routes. They go out to both learn about the world and to develop their own characters.
Of course, these are hardly the only two great walks in the world – actually, the most popular great walk nowadays in the Camino Santiago in Spain. I don’t know much about the Camino, but here is a comparison of the Shikoku Temple trail and the Camino and here is a comparison of the Appalachian Trail, the Pacific Crest Trail, and the Camino.