In the Model S, the primary factor is that the car is sending a signal to the fob, so the fob's low-power receiver has to be close enough to "hear" it and respond with the proper command. If instead you just click the fob, it transmits the command immediately. Now whether it transmits with a more powerful signal in this "active" mode vs. the "passive" mode of the car triggering action, that is unknown.
In the Model ≡ , while BT LE can track distance, the question of whether it is implemented is a good one. We shall see in a couple weeks. I would hope Tesla would take the time to code that in given all the S/X complaints of their mirrors unfolding when people walk through their garage. Now you couldn't even counter those people with "why do you walk around with the fob in your pocket?"