What would you do? Climb towards another conflicting aircraft that you don't see but ATC does? Or avoid him, descend towards an aircraft that you do see, and hope to avoid him using visual means?
Please give some good reasons for your answer that will also be good reasons for any other pilot in this situation.
To be sure, I wouldn't be maneuvering opposite the RA! I might do nothing and depend on the other crew's compliance with their RA for separation; to mitigate the hazard, I would probably climb 300' just to offset my flight level. It would be an instinctive, reflex action . . . nothing to think about.