I haven't done it myself, but everything I've seen says the AT is a completely different kind of experience. You need to (should be) in reasonably good shape, you have to carry a lot more gear (ties into the first point), there's a lot more planning and logistics to work out, and it's a much more rustic experience (literally camping every night, with a few hotel stays).
For the Camino, I started out 40 pounds overweight, I did zero physical training in preparation, I had to plan basically nothing except my flight, arrival day and departure day. I was able to do it with literally only a few weeks notice (I had never heard of it until a month prior.)
Ultimately what I'm saying is the Camino trails are much more accessible to a wide range of people, as long as they're able to fly to Europe.
ETA: I should perhaps explain that the Camino trails, or at least the most popular trail I took (the Francis) is really more of a walking trail than a hiking trail. It's mostly flat(ish) and is much closer to what's depicted in pictures posted on The Great American Rail-Trail.
Appalachian trail is pretty much wilderness unless you pop down to a town. Whereas the trail for the Camino de Santiago, at least the part that I was on, constantly sent you directly through towns.
The US basically has more options for long distance backpacks where you're mostly camping. Parts of Europe offer more options for town to town (or hut to hut) walks that are often not that strenuous and may even have luggage shuttle options. One isn't better than the other but they are different in general.
There's probably lots of stretches where you need to go more than 10 miles to hit much of anything. There certainly is on long hiking trails in the Midwest and West.
Doing a quick search, there's spots where paved roads are 30 miles apart, and lots of times it will be more than 10 miles to get to the nearest town.
For the Camino, I started out 40 pounds overweight, I did zero physical training in preparation, I had to plan basically nothing except my flight, arrival day and departure day. I was able to do it with literally only a few weeks notice (I had never heard of it until a month prior.)
Ultimately what I'm saying is the Camino trails are much more accessible to a wide range of people, as long as they're able to fly to Europe.
ETA: I should perhaps explain that the Camino trails, or at least the most popular trail I took (the Francis) is really more of a walking trail than a hiking trail. It's mostly flat(ish) and is much closer to what's depicted in pictures posted on The Great American Rail-Trail.