I'm pretty sure both sides rigour in claiming kills was about the same and overclaiming was roughly even. I read a comparison recently of scoring rates of a couple of Allied aces and it matched the rates of many German aces. The only difference being the amount of time they were allowed to stay in the combat arena and scoring opportunities available to them. The Allied pilots were generally rotated and rested throughout the war so had much less opportunities to score. Also, many of the German aces served on the Eastern Front where scoring opportunities were much greater and don't forget that nearly 90% of Germany's casualties occurred in the East.
Unlike the Allied pilots, the German pilots generally had to stay in combat until they dropped, so either got very, very good, or very badly injured/dead. Scoring opportunities for Allied pilots against a waning Luftwaffe also tells a story. Towards the end of the war (when the bomber crews were unofficially being used as live bait so the fighters could engage and annihilate the Luftwaffe), things changed. The experienced German aircrews could not be replaced and quality suffered and by early 1945 the Luftwaffe effectively ceased to exist.

