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.