Yes, a person on an airplane at 4 miles above sea level would experience time dilation differently from a person at 4 miles elevation in the mountains. The effects of time dilation are influenced by both relative motion and differences in gravitational potential.
Regarding relative motion, if the airplane is moving at a significant fraction of the speed of light relative to an observer on the ground or in the mountains, then time dilation due to relative motion would come into play. However, in most commercial aircraft scenarios, the speeds are not substantial enough for significant time dilation effects.
On the other hand, gravitational potential does have an impact on time dilation. According to general relativity, time runs slower in regions of higher gravitational potential. So, a person at 4 miles elevation in the mountains, being closer to the Earth's center and within the Earth's gravitational field, would experience a slightly slower passage of time compared to a person on the airplane at the same elevation.
The effect of the mass of the mountains on time dilation would indeed counteract (to some extent) the elevation/time dilation effect caused by the difference in gravitational potential. This is because the mass of the mountains contributes to a stronger gravitational field, which causes time to run slower. Therefore, the person at 4 miles elevation in the mountains would experience slightly less time dilation compared to what would be expected based solely on the difference in elevation.
However, it's important to note that the difference in gravitational potential between an airplane at 4 miles above sea level and a person at 4 miles elevation in the mountains is relatively small. The impact of this difference on time dilation would be extremely subtle and likely not practically measurable in most everyday situations.