Very cool stuff! I could be wrong but while the Germans are definitely getting the better of the Brits in air to air engagements
it looks like this may be at least partially due to the type of mission each side is performing i.e. the British seem to be attacking bases and other German assets on the ground alot more than Gremans and Italians are British ones.
If your lumbering off to battle with a 500 lb bomb strapped to your plane or just spending a larger portion of your time down low straffing assets on the ground thats going to put you at a big disadvantage in air to air but could still be advantageous overall in terms of winning the campaign.
You are both right and wrong. In a larger sense you are right - the British Strategy is focused on the ground war first and foremost, and secondarily on destroying Axis assets including their air bases, ships, air transports and other communications and logistics. Effectively though, especially during the battles, they are ignoring the Luftwaffe and concentrating on attacking the Afrika Korps.
However at this stage the British fighters are not yet carrying bombs themselves. The bombing is being done by Marylands, Bostons and Blenheims. I am not sure (and in fact I don't think) they ever did put bombs on Tomahawks, though the Kittyhawks were already there by December and would soon be flying with bombs (allegedly at the insistence of Clive Caldwell who did some of the first flying tests with Kittyhawks and Hurricanes carrying heavy -250 kg+ bombs to prove the concept.)
The British fighters were flying four kinds of missions - fighter sweeps, what you might call 'free' escort, close escort, and strafing. Close escort was the most dangerous because to keep formation with the bombers, the British fighters had to slow down to the cruise speed of the bombers. This was Caldwells big beef - the cruise speed of a Blenheim was about 95 knots IIRC. Way too slow for safety when enemy fighters are around.
In the 'free' escort and fighter sweep missions, the British were still making two fundamental errors - flying too low, at around 6,000 - 10,000 ft, and flying bad formations. The biggest problem with the formations was they still weren't flying in pairs, but rather Vics of three. The second issue was that they hadn't worked out any good system for responding to being bounced. They flew with 'weavers' roaming back and forth above and behind the formation, who were easy pickings and whose constant movement made the whole formation easier to pick off from a distance, and they often revered to Lufburry circles when attacked which put them on the defensive and was also deemed to be a mistake.
Strafing missions were often done after other combat (such as during a bomber escort), before returning back to base. Sometimes they were more organized as the main mission so to speak.
The Germans were better organized, flew in pairs / finger four flights and fought basically two ways - the first in small groups, often flights of four who would go on a 'free hunt' and pick off 'weavers' and stragglers in bounces from above, covering each other and using their altitude advantage to break off. Due to the defensive tactics of the British they could often get away with this without much risk. The second were much larger and more coordinated attacks in which they would often manage to achieve local air superiority by concentrating multiple units in an attack on an RAF squadron or two. In this manner they repeatedly achieved massacres of Hurricanes knocking down 8 or 10 in a single engagement. This backfired on them somewhat against Tomahawk units a couple of times though such as on Nov 22 where they had a substantial numerical advantage but still took unacceptably high losses.
It was more rare but they did also sometimes launch big Stuka or Ju 88 missions against Allied troops or airbases, sometimes in coordination with the Italians and these days often blew up into big brawls.
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