Based on the stats the allies had a mixed bag in the air. They actually inflicted quite a bit of damage on the Axis in the air and especially mauled the Axis Bomber force (destroying 62.8% of the Axis bombers to a loss of only 36.1% of their own bomber force). Both sides actually loss the same number of fighters (70 each) but the Axis deployed more fighters than allies, 163 to 126. So I would have to say the air war goes to the allies.
However, the allies were not able to prevent the Axis from getting their bombers to target and disrupting the attack of those who did get to target. As shown by the Axis destroying a combined average of 72% of their targets.
Also while the Allied bombers suffered less losses in the air (39 out 108 B26s lost, 36.1% loss rate) their bombing results was not as good as the Axis. They only destroyed a combine average of 51.4% of their targets. So either their accuracy was off or Axis fighters were still engaged over the allied targets and were able to disrupt the allied bomber runs more than their counter parts did over Axis targets.
Basically the ground war went to the Axis.