Some thoughts on the subject:
The key difference between a microphone and an antenna is that the microphone is sealed from the back - it senses a pressure difference between the front and the back of the membrane regardless of the extent of that pressure region.
If you have a small membrane that is not sealed from behind, then at low frequencies it will "bathe" in the slowly varying pressure and will indeed show little signal; a larger membrane would prevent the pressure from "leaking around the back" and thus be more efficient at capturing the energy from the incident sound wave. It is true that a larger membrane can "harvest" more energy - but typically the transducers are so effective that they don't need to be large in order to get a good low-noise signal pickup.
A conventional antenna is immersed in the electromagnetic field - current induced depends on the potential difference from one end to the other (integral of electric field). This value increases with increasing length of the antenna until you reach a quarter wavelength (for a monopole) or half wavelength (for a dipole).
In this context it is worth noting that the lateral displacement of the membrane is very, very small - in other words, the membrane won't move enough to compress the air behind it.