The pilot receiving instruction and flight instructor of a single engine low wing airplane were completing a preflight engine run-up in the designated run-up area. The pilot of a tailwheel-equipped biplane after landing was cleared by the tower controller to taxi to the company hangar. The pilot of the biplane stated that while taxiing, he failed to make S-turns to improve his forward visibility due to the tailwheel configuration. The pilot of the biplane reported that he never saw the other airplane until making contact. The flight instructor stated that by the time they saw the biplane, there was not enough time to take evasive action before impact. The low wing airplane sustained substantial damage to the right wing, and the biplane sustained substantial damage to the lower right wing and wing struts. Both airplanes’ pilots reported that there were no preaccident mechanical failures or malfunctions with their corresponding airplanes that would have precluded normal operation.