I know we wouldn't have Patton's blitzkrieg across France. This is because his forces would have been trying to take Antwerp (which took the British/Canadian forces some time to do). Could Patton have done it quicker? Would Montgomery be taking his sweet time crossing France?
Interesting question. I think eventually it would have come down to who got the fuel right? The Germans always made the comment about how the Brits were more efficient fighters and especially hellacious defenders while acknowledging that the Americans seemed to grasp mobile warfare much better or quickly. So perhaps it could be argued that Patton might have been more aggressive about pushing through faster, crossing the Rhine, and making some kind of bid for Berlin eventually. The biggest thing that comes to my mind is that there would have been no Market Garden as OTL.
My imagination runs wild with thoughts of a fast hard push straight toward the Rhine, crossing around the Ruhr fork (Say Durisburg). Bradley sends Patton (with Simpson) and strong elements hard south straight into the flank of any units along the Rhine's eastern bank. A large part of the Ruhr industrial region, the cities of Cologne and Dusseldorf, and large numbers of confused and scrambling troops are captured (or essentially encircled) before the Allied troops are temporary stopped around Frankfurt and the Main to consolidate. Only a matter of time before the Germans are forced out of Strasburg and the British cross and push to Stuttgart. Meanwhile in the North, Hodges is sent north to successfully flank or liberate as much territory in and around Holland as possible. While both sides rush to adjust to the sudden realignment of the entire Western front, there are talks within the allies concerning a massive airdrop behind the Elbe once forces get within proximity of Hamburg or the River.
Okay ... sorry got carried away. Without a Market Garden would the overall strategy change with an American North?