Ummm. Hitler's DECIDED for the Caucusus. No serious attempt was made to take Moscow after winter set in in 1941. The Schwerpunkt of the German effort of 1942 was the Caucasus because that is what Hitler wanted. Hitler may have been militarily inept, but he knew that Germany wouldn't last without those oil fields.
The Germans were outstanding in defense at Normandy - remember they never committed their Panzer Divisions or other first rate units and suffered from a total lack of air coverage. I'll bet on enfiladed 88's vs. T-34's.
Once the Germans were winkled out of the hedgerow country (a seriously difficult task), they had no place to go but back to Germany. Rommel knew his tanks were toast against allied tactical aircraft when they were in open country.
BTW, I'd take the T-34 & lay the Mark VI Tiger. Too heavy for offensive operations, and too expensive to produce in numbers.
The Mark IV Tiger was also a bitch to maintain.