Gamma rays are "more powerful" than radio waves only in the sense that the photon energy of the former is much higher; "gamma" radiation is usually taken to mean electromagnetic radiation arising from decays of atomic nucleusses and other nuclear processes; they have a wavelength of well less than a nanometer, whereas AM radio waves have wavelengths of hundreds of meters. A typical gamma photon energy is of the order of $1{\rm MeV}$; an optical photon is of the order of a few ${\rm eV}$ and a radio wave of the order of $10^{-8}{\rm eV}$.
Radio waves are easy to make at high powers - tens of kilowatts - with alternating electric currents produced by primitive electronic technology. They are also easy to modulate, i.e. to have a signal encoded onto them- with the same technology using sophisticated modulation schemes. The effects of such waves of even these powers on biological systems is very mild. Gamma rays of this power are hugely expensive to produced with human technology; only nuclear processes will make them. They can only be modulated by mechanical means - deflexion from mirrors and shutters, so would be useless for high speed communication - of the order of ${\rm GBps}$ which we nowadays routinely achieve with radio technology. Gamma rays of this power are utterly lethal to any biological system in their path. Moreover, their high photon energy means that they interact with and are swiftly (in comparison with radio broadcast distances) absorbed by air. They would be useless for terrestrial communications from this last point of view also. Radio waves, with their low photon energy, have very little interaction with clear air.