That depends on how you define "commander." How high or low do you want to go? For example, Patton commanded Third Army in Normandy and beyond, but he was subordinate to Omar Bradley's Twelfth Army Group, who himself was subordinate to Eisenhower - should Third Army's casualties be credited to Patton, Bradley, or Eisenhower? How about even the corps commanders being credited with those casualties - V Corps and XII Corps probably had as many men as any Soviet field army of the same period (Soviet divisions and corps being smaller - a Soviet tank corps was roughly equivalent to an American armored division), and so Patton or Hodges were probably commanding forces more equivalent to a Soviet front.

However, my money would be on Chiang Kai-Shek, who held direct operational field command during the Battle of Shanghai (280,000+ casualties) and the Battle of Wuhan (200,000+ casualties). Those nearly 500,000 casualties include almost as many military deaths as the Americans or British lost during the entire war, which should also give an indication of the scale of the fighting in China during the war. It'd be awfully hard for any American or British commander to equal these totals.