S!
Dieppe was in summer '42, shortly after the 190A4 had come out with the BMW 801 now running at full boost. At that time, the A4 was easily the superior to the Spit V, as the A5 is its superior in AH. The 109F4 was also present, what many perceive to be the pinnacle of 109 development vis a vis its opponents, and was no slouch, with a superior climb and top speed, and maneuverability not far off the Spits in the horizontal.
Plus the Brits were still using Hurricane IIC's, which in enviroments where spotting your opponent is much more difficult than in AH, suffered tremendously from its lack of speed and climb. The Hurricanes were also carrying ground attack ordanance in many cases, as they were the "Typhoons" of their day, which made them even more vulnerable.
This was because the British were focused on ground support for the landing, which meant they were operating at low levels, while the Luftwaffe was focused on disrupting the ground support which meant they almost always had the height advantage.
Plus the Luftwaffe bases were closer to Dieppe, which meant the Luftwaffe could refuel and re-up faster.
That answer your statement?
Finally, the Luftwaffe didn't "hand the Brits their a**es", they inflicted more losses, but suffered quite a few of their own.