Most of the communication on Earth and to-fro Space takes place over low frequency visible, infrared, micro and radio wave spectrum of the electromagnetic spectrum.
The immediate benefits of using low frequency EM spectrum which I think of are as following:
- They are not blocked by Earth's atmosphere and magnetic field. On the other hand, cosmic rays which consists mostly of high energy electrons, protons and ß particles carries electric charge and magnetic field. Hence, they will be hugely affected by Earth's magnetic field. Maybe setting up receivers and transmitters at poles helps a little.
2.Speed: EM waves travel at light speed, cosmic rays always travel at lesser speed which brings me to the next point.
- Energy needs: The energy required to generate radio waves can be provided by low power solar panels. However, to generate cosmic rays one would need a particle accelerator. Something like a portable LHC, which I don't think is feasible. Moreover, if you want to generate faster cosmic rays then you have to put in more energy.
I can only think of these constraints at this moment. I don't know if sending information via cosmic rays carries any advantage.