Energies carried by electric and magnetic fields in plane waves
An electromagnetic wave carries energy. That's the fundamental 'currency' of physics. This energy is carried in both electric and magnetic fields.

If we measure the amplitude of each field, and find their ratio is 377 ohms, this tells us as much about the specific units we have chosen to use to make the measurement as it does the fields themselves.

You can launch and intercept an EM wave with either an electric dipole, or a magnetic dipole. They both couple completely to the energy-carrying wave in the far field. They are different in the near field, where the non-travelling component of the fields is more nearly electric or magnetic respectively.

For any given antenna configuration, you can define an effective area (at a certain frequency, in a certain direction) that designates its coupling with the far field. In some types of antenna, for instance a parabolic reflector dish, what contributes to the 'area' is obvious. In other types, a Yagi array for instance, the 'area' increases as more elements are added in the direction of the wave. Different configurations will have different physical size to electrical area ratios, it's more the specific configuration than whether it's primarily electric or magnetic that controls this.

In the absence of losses, the power output from an antenna is equal to the energy it intercepts from the wave. For small antennae like a short electric dipole or small area magnetic loop, their terminal impedance will be high or low respectively, so if you restrict yourself to measuring their current output, the outputs will indeed be different. Instead, measure the power output into a matched impedance.