Who “got more radiation” in terms of biological effectiveness for radiation damage and (b) by what factor?

Your group is a radiology department in a hospital. Two patients in your waiting room are arguing about who “got more radiation” in their cancer treatments. Patient A received 2.0 Gy of radiation, while Patient B received 1.0 Gy. Patient A is claiming that he had twice as much energy delivered to his body based on these numbers. Upon further investigation, it is determined that Patient A received radiation from fast neutrons, RBE 10, affecting 22 g of tissue. Patient B received alpha particles, RBE 18, affecting 30 g of tissue. (a) Who “got more radiation” in terms of biological effectiveness for radiation damage and (b) by what factor?