Dave Shrader wrote:
"Help me understand what you are trying to say."

I`ll elaborate.

Efficiency is output / input.

1/2 or more of the power received by a receiving antenna is re-radiated.

Nearly all of the power received by a transmitting antenna is
transmitted.

Considering the energy available to the antenna, the job done by the
transmitting antenna system as compared with the job done by the
receiving antenna system, the transmitting system is better.

A receiving antenna must be resonant to enable full acceptance of
available energy, and it must be matched to avoid re-radiation of more
than 50% of the energy it is able to grab.
If off-resonance, the receiving antenna has too-high impedance for
significant induced current. Of course, we have such good receivers we
can do without good efficiency.

A transmitting antenna will radiate energy proportional to the current
in the antenna.

Ronold W.P. King says in "Transmission Lines, Antennas, and Wave
Guides":

"---the power (Io squared)(Ro) supplied to a highly conducting antenna
(of Copper), with Ro taken from the curves of Sec. 10, is for practical
purposes all radiated to the more or less closely coupled universe
outside the antenna, while that used in heating the antenna itself is
negligible." This information is on page 113.

Inefficiency is to be found elsewhere from the transmitting antenna
itself. We may use inefficient transmission lines and our wave
generator, the transmitter, may be inefficient. We usually try to keep
their losses low.

It is not uncommon to produce RF in a Class C amplifier with an
efficiency of 70%. With reasonable lines and antennas, nearly 100% of
this power output can be radiated, producing appropriate millivolts per
meter at one mile from the antenna.

This is not completely reversible due to re-radiation of 1/2 or more of
all the power a receiving antenna can grab.

The hope for point to point wireless power transmission is in using
antennas like large dishes, for example, which concentrate power within
such a small angle that the receiving antenna captures all the
transmitted beam. Similarly, all re-radiated power is beamed back to the
transmitting antenna for another trip to the receiver.

Best regards, Richard Harrison, KB5WZI