Well, by definition, the hills are higher because the peaks are at a higher elevation. All the relief nonsense is just about the fact that the base of the Appalachian hills are narrower. The Appalachians seem like a longer range until you realize that the Black Hills are considered by geologists to be part of the Rockies range. The biggest claim the Appalachians can make is that they are older.
The people who named the Appalachians had not seen actual mountains yet, so they didn't know any better, bless their hearts. By the time white folks saw the Black Hills they had already seen the Rockies, so in comparison, they seemed like hills. East coast bias has been here since the Pilgrims landed.