ETO January to May 1944.
Since the reported Luftwaffe losses include accidents on combat sorties and losses on non combat sorties, if you really want to calculate some sort of total cost of air war in terms of aircraft total losses. Luftflotte Reich 2,217 day fighters lost, 8th Air Force 1,615 heavy bomber losses on operations and around 135 not on operations. My losses list says 75 B-17 non combat mission losses (includes lost on ground), with a similar but smaller number of B-24. Thereby arriving at 1.27 all cause fighter loss to 1 all causes heavy bomber loss.
If you just want to do combat losses and assume USAAF other cause losses were not caused by the enemy, then it is 1,440+216 = 1,656 to 1,459 or 1.13 to 1. Assume the other cause losses were say flak and fighter combined, battle damage of undetermined origin etc. and it is 1,656 fighters to 1,615 bombers, 1.025 to 1.
Since most attention is on combat caused losses and again assuming the USAAF other cause figures are not combat related then the 5 months of air combat January to May 1944 cost the USAAF 1,459 heavy bombers and 780 fighters, total 2,239 against Luftflotte Reich 1,620 day fighters, the Germans clearly won in terms of number of losses, won bigger in terms of cost of lost equipment and very much bigger in terms of personnel casualties. Drop that to air to air combat only, assuming every Luftwaffe fighter combat loss was a shoot down, it is 1,569 USAAF losses to 1,620 Luftwaffe, almost even, with the Germans ahead in material terms and way ahead in personnel terms.
The Luftwaffe put up a strong defence of Germany in the first months of 1944 but could not replace its personnel casualties while keeping up average aircrew quality, the USAAF could.
All this of course excludes Luftflotte 3, the RAF and the reality an increasing number of USAAF fighter losses were not on heavy bomber escort missions as the 9th Air Force switched over to invasion preparation. It means all the above are guides, not absolutes, to the way the Luftwaffe day fighter force did not go away without a long fight which cost the USAAF in particular a great deal.
With nothing else in the sky, nor flak nor things like vultures present (they shot down a number of Hurricanes in India, though the Hurricanes always shot down the attacking vulture) when a Luftwaffe fighter formation and an 8th Air Force heavy bomber formation fought each other in 1943 on average 2 fighters were shot down for 3 bombers, in early 1944 that shifted to 1 fighter to 2 bombers. The USAAF damaged aircraft reports noting the increase in average Luftwaffe fighter firepower in early 1944. The numbers are as explained pure air to air, fighter versus heavy bomber, nothing else.