When I think about the differences between the AT, the PCT, and the CDT, I don't think so much about the footpaths or the mountains.
Sure, there are differences between them. The mountains of the PCT and CDT are much higher. The AT's climbs tend to be steeper, however, especially in New Hampshire and Maine. The AT's footpath is also more rugged, with long stretches covered in roots and rocks.
Instead of those things, I mostly think about the differences in the water. The climate in western states is much drier. That includes more than just the deserts of California and New Mexico.
One indicator of this for me is the number of water sources. They are fewer and farther apart on the PCT and CDT than on the AT. Another indicator is rain. Though some precipitation fell on parts of the PCT and CDT, I experienced many more wet days on the AT.