I wonder. I don't think favoring China instead of Japan has any effect on either the Battle of Britain or the Battle of North Africa, and I'm not even seeing how the Battle of Britain affects the Battle of North Africa. For that matter, I'm not even certain of the effect of the Battle of Britain even on the RAF in Britain itself, much less North Africa; the entire month where the Germans were attempting to attack the RAF directly via bombing runs on air fields in the south resulted in the temporary shutdown of a single station (Biggins Hill), which was restored to operational status in two hours. The problem with the Battle of Britain was never the air fields; even if worse had come to worst, they could and would have redeployed northward to Scotland to preserve their active force, using southern airfields primarily to rearm and repair on the fly. It was that the Germans could not replenish their losses as well as the British. Fighting over Britain meant that every parachuting British pilot returned to the fight, while every parachuting German pilot was lost to the war as a POW (if lucky; those who bailed over the Channel or the North Sea, in the brief case of Luftflotte 5's operations) - civilian repair services put almost 5000 planes back into commission between July and December, once they got into gear. British planes, if damaged, didn't need to fly as far for an emergency landing. British planes low on fuel or ammunition could rearm and return to the fight without a trip across the Channel. Crew-wise, German fighter forces tended to have around 50-65% of their operational crews by the raw numbers by mid-September, and in the single month of August, they had lost almost 20% of their actual aircraft frames. These were all key factors in the reasoning behind shifting to nighttime raids in September, which were less effective. While the Germans may have managed to do more damage by focusing on the operational destruction of the RAF, it was unlikely to be more than a pipedream, continuing to deplete the cream of the Luftwaffe, and the Germans would have run out of planes before the British did.
As for how it affects North Africa, I'm not certain. Rommel, by El Alamein, had already overreached his supply lines. The Allied air force in theatre had always received obsolete and outdated craft that wouldn't have served well in the air defense of the British Isles, including American lend-lease. Moreover, they always outnumbered their German and Italian counterparts, even after the deployment of the Afrika Korps. Key forces in the DAF were never going to be deployed to Britain for political reasons, either (read: the South Africans threw a snit). Unless the Germans miraculously take far fewer losses than the British, it's unlikely the Regia Aeronautica alone will make up the difference.
However, as noted, I'm not even certain how a choice to retain the Chinese mission plays into this. Taking it separately for that reason, it's key to note that the Japanese will enter war with the Western Allies in either case; the political pressures at play (namely that the US does not want to see all of China vanish into Japan's gaping maw, and that the Japanese are still going to see that the British and Dutch are too occupied - literally, for the latter - in Europe to defend their Far East holdings) are not going to disappear just because of the German mission in China. Indeed, US involvement with China may well actually end up similar to Soviet involvement with Bulgaria; a bit of a "quid pro quo" mutual non-aggression for most of the war where China/Bulgaria doesn't actually declare war on the US/USSR. German aid to China was rather reliant on the USSR once the Sino-Japanese War began, and thus would end with the onset of Barbarossa in either case. It was never all that major in absolute numbers as well, and would be unlikely to help tilt the balance of the war towards China any more than US or British aid to China (the Flying Tigers) did (or didn't) historically. German promises were grandiose, but it's difficult to see how they would have materialized once the Sino-Japanese War began, much less after the European War or Barbarossa. Likewise, US aid to the UK was operating without any concern for the Japanese, and several US destroyers had already engaged their German counterparts in the North Atlantic before war was declared (most famously, the USS Reuben James was sunk by a German U-boat with the deaths of over two-thirds of its crew); continuing bleeding along these lines would inevitably have brought the US into the war against Germany. Moreover, US aid to the USSR was also unaffected by the historical war between the US and Japan. Operating under Soviet flag, the Japanese permitted the shipment of US supplies to the USSR even during the peak of the Pacific War, accounting for half of all Lend Lease to the USSR. While direct war materiel was not permitted, locomotives, rail stock, trucks, and the like were not considered war materiel, nor were radios, electronic equipment, or canned foodstuffs (read: rations), which all proved invaluable in maintaining Soviet logistics. I see no reason why ongoing German-Sino cooperation would change this. The USSR actually gains additional reasons for its ongoing aid to the GMD pre-Barbarossa: now, they're also supporting an ally of their German friends. They're also simultaneously invading Xinjiang, but those are mere details that also won't change in this timeline, any more than they did historically. As for Barbarossa, by 1941, the Japanese control most of the Chinese coastline and northern China, the best-trained and most-reliable forces available to Chiang have been destroyed outside Nanjing and Shanghai, and the Chinese have largely completely withdrawn to the western interior. The Chinese, even moreso than the Japanese, have a very, very good reason to not involve themselves in any invasion of the USSR under these circumstances: they have no ability to do so. If anything, if the Japanese are sufficiently anti-German, Stalin may authorize an earlier draw-down of the Far East command's strength in order to reinforce the German front. While the involvement of the Siberian divisions is rather overstated due to reliance on German sources (which notoriously underestimated the USSR - the logic goes "well, we thought they could only raise such and such a number of divisions, but we're facing close to twice that; rather than our assumptions being incorrect, they obviously pulled these extra divisions out of Siberia"), they can't be entirely discounted, either; even the 28 divisions historically transferred were not insignificant, especially as they were already winter-ready and trained for snow operations.
The biggest major advantage to the Axis, I think, is rather straightforward: the Germans will not declare war on the US after Pearl Harbor. This buys them a few months to a year in which US is not fully involved in the war, but given how US involvement in the North Atlantic is increasing and the excuse for "Ameri-British cooperation against the Japanese" pushing a cooperative military agenda, I'm hesitant to push it any further beyond that. I'm not sure, however, how effectively they can capitalize on this opportunity; by December 1941, they're already stuck in the USSR. Indeed, without the US actively mobilizing for war, the US is actually free to increase Lend-Lease shipments to the UK and USSR even further without diverting supplies to their own armed forces. As for China itself, the US ends up trusting Chiang even less than they did historically (as hard as that is to believe it possible), but the common enemy of the USSR and ChiComs still likely drives the two together in the post-war world.
EDIT:
Oh, I thought of something else: tungsten. Historically, the majority of German tungsten was sourced in China, and without a renunciation of the Chinese mission, that trade would continue for a time. However, looking it up, the trade collapsed not just because of the diplomatic situation, but also the military situation: with the Japanese capturing most of the ports, China simply couldn't ship its tungsten anywhere. If Germany sticks with China, Japan won't let Chinese tungsten or German payments cross their front lines to go through the ports. If Germany sticks with Japan, all the tungsten mines are still in the Chinese interior under Chinese control. It's rather a horse apiece.