Now having played these two games for several more rounds there do appear to be some disadvantages.
Sacrificing german planes to take CAU, or Italian troops on a first-round assault to help the Germans take it, combined with placing fewer troops in Africa - can make it so that the Axis has less of a fighting force, and might also be making less money than otherwise possible.
Italy is likely to lose its NO(s) in Africa faster. Germany gets the CAU NO, but if it is possible to get this by trading KAR, then that might be a lot easier.
Germany loses a lot of flexibility by being tied into sending armor to CAU (either to reinforce it, or to take MOS). Also fighters can get tied up too, making atlantic Allied convoys easier and facilitating the US going for Japan.
Plusses: if you can get Italy to fight your Russian territory border skirmishes and to build infantry to defend ITA, FRA, and GER against the Allies amphibious assaults - then Germany can build up much faster than Russia and ultimately take Moscow with a stack of armor (possibly reinforced by a buy of all bombers, the turn before the assault - as they can fly from GER to MOS is one turn).
Having Italy use its infantry for cannon fodder is much better than having Italy attack MOS to soften up the defenses before the German attack, as Italy will typically lose all its units on the first round of fighting (thus it costs 10 IPC to kill a single defending Russian infantry - by buying 2 arm, or 10.5 with inf/art). Italy can also intentionally escalate in border countries (stack an empty country with 2 inf, instead of 1) to bleed off more Russian units.