This may seem like a stupid question...
Most airports do not use the same landing strip depends on weather and air traffic conditions. I do recall that when landing one side the airplane can clearly see the glorious Tetons the other side does not have the same opportunity.
Is is just a luck of the draw as to what side of the plane you happen to be sitting on and what landing strip is used on that particular day?
Either way flying to Jackson is a terrific experience landing at the base of the mountains.