When I was working on my master as a geology [IN Univ], I thought the apparent difference in aging (due to the topography of the ranges)could be attributed to the climate on the west vs the east coast. Not putting any time into this idea, it could be fairly easily evaluated by comparing other mountain ranges under differing climatic settings. That being said, we should remember that dramatic shifts in climate in very recent history can be ascertained in the written records of Herodotus, Scripture, and other sources noting that areas that were once extremely fertile (again within historical times), and now completely desert and barren. This is verified by archaeological studies in many now desert.
Although we might be tempted to attribute the structural difference of the Rockies and the Appalachians to the differing tectonic on the coast, the obvious factor is one of weathering and erosion, not the mode of mountain building.
To recap, more weathering (Appalachians) could indicate a greater age in an old Earth, or a consistently wetter climate in the eastern continent in a young Earth scenario.
We don't often realize that there were more globally catastrophic events than Noah's flood. Scripture describes Earth originally created with one continent/one Ocean, the Pangaea/Tethys Sea of science. Scripture also refers to the division of Earth in the time of Peleg, which we normally assume to be a societal division, not a continental division as well. We might see hints, too, of the ice age, in the various mention of famines in the times of Abraham, Joseph, and ancient secular histories, such as in the Histories of Herodotus (et al). This last evidence might seem to be too von Daniken-ian to be credible, but if we look at the overwhelming evidence for rapid changes in Earth it becomes credible.
There separate dramatic global changes are clearly undeniable: the existence of a single continent undergoing violent structural damage (Flood), separation of the continents creating mountain range and basins of deep deposition (Peleg / Babel), and ice ages (global famines, sea level changes, desert formation, dramatic loss of species). The basic difference between a scientific v Biblical interpretation of geological evidence is a matter of time (billions v thousands of years) and paradigms (atheistic scientific v Scriptural). Sadly creationists began by failing to recognize the other major, but separated events of the division of Earth, and the rapidly ensuing major climate changes, and that created confusion as to just how much and in how many different ways the earth has been altered, so our interpretation of the geological data was skewed and incorrect, making our overall conclusions rightly vulnerable to scientific scrutiny.
During my time in geology, I found a curious fact. Very often when a geologist was converted, it was an easy step for them to abandon the evolutionistic old Earth paradigm for a young Earth creation view. And the same went in the other direction. This showed me the inherent spiritual nature of how our beliefs change with our spirit.
I dropped virtually al my interest in this debate, after I discovered the powerful apologetic tool used by Christ and focused on that: the work of the Spirit in His works of Love by healing us in body, soul, and spirit.
Eternal Blessings