This would be a tough one to answer. The various Allied militaries were distinctly different in their mindsets and doctrine fromt that of the Germans. Let me start with the easy ones:

In the air the switch is distinctly in favor of Germany now. The Allied states are saddled with a raft of incompetents and technical illiterates starting with Göring and going down the list. Officers like Kesslering would go unappreciated. While an excellent ground commander, he is nothing special with air power.
On the flip side LeMay, Harris, or Kenney to name just a few, would have quickly changed Luftwaffe policies making that force far more coherent and effective than it historically was. At higher levels, the orgainzation of production and aircraft design would have quickly done away with many absurd and failed projects in a heartbeat. I could see the He 177 ending up with four engines, no dive bombing ability and being an actually effective aircraft to give one example.

At sea the narrow-minded hidebound conservatives of the Kriegsmarine would likewise be replaced by a better crop of far more aggressive and knowledgable Admirals from both the British and US Navies. While they would have far less material to work with they would know better how to utilize it than the now rich German admirals would with Allied naval units.

On land, the Germans would likely run circles tactically and operationally around most their Allied counterparts given the plethora of material they now have. However, they would most likely also be far less conservative with it and far more willing to trade casualties for victory than the Allies were. The only big advantage the Germans get is in now having far more genius for strategy and logistics than they had. I can't see the Allied generals in this situation getting themselves repeatedly pocketed and destroyed on an immense scale. Nor can I see them squandering resources or meddling with production like the Wehrmacht did so frequently.
For example, the Allied generals would have never reinforced the obvious defeat in North Africa as the Germans did.
And, Roosevelt and Churchill did meddle in strategy on a frequent basis. However, they, along with Stalin, did not do so to the degree Hitler did.
On the whole, I doubt that the changes on the ground would be world shaking but rather give the Allies a marginal advantage in operations they originally did not have.