Alternate 'Overlord' US Forces are swapped with British & Commonwealth, what's the consequences?


Inspired by my thread "Alternate Battle of Midway' RN instead of USN'

What if US Forces are swapped with British & Commonwealth Forces at D - Day, so each force does what the opposite did and face as in OTL??

What are the probable consequences with the alternate dispositions?
How different would the campaigns of both the British & US change?
How would the original landings change if the US had Gold, Juno & Sword beaches and visa versa?
What would be the effect of having alternate air drops compared to OTL?
What would be the effects on the German forces and their responses?
The POD lasts all the way through until the liberation of Paris

PS: Both sides still have to work with the same troop numbers, same weapons, same inventory as in OTL.

Much obliged!
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I take it the German forces are positioned as OTL.

Unless the US assault forces are beefed up it would be tricky to give them three beaches. But which two of the British and Canadian ones should they land on?

Giving the Americans Sword and Juno leaves a Commonwealth force assaulting alongside them at Gold beach. Is that practical? But giving the US the Juno and Gold sites leaves a Commonwealth formation at Sword separated from the rest of their forces.

So probably Sword and Juno?
perhaps the priorities are changed, and instead of one landing beach on the Cotentin there are two, (it is large enough), so you have the forces that would have landed on gold and Juno instead hitting Utah and another beach further north with the intention of racing to capture Cherbourg as soon as possible. The Americans meanwhile go to Juno and Gold, and no landing is made at Sword.
I would swap the British at Sword for the Americans on Omaha and the Canadians on Juno for the Americans on Utah. This helps the British co-ordinate and link up Omaha and Sword beaches. Also on Omaha the DD tanks will be launched inshore and get to the beach to support the assault unlike OTL. Hobards 79th Division will also be very active!! The troop numbers in this swap are close enough to be viable. However can you see the Americans pulling off Pegasus Bridge?
Wasn't a major reason for the deployment that it reflected the other side of the channel better, i.e. it matched the locations of the forces and their supply dumps. If that was the case, switching it, will make logistics worse.

For the outcome of the landings it wouldn't make much of a difference. Maybe the British perform a lttle better at Omaha, because as mentioned they had more armour and a better grasp how to use the DD-tanks. With different beaches assigned, the forces will adapt to their mission, as @marathag suggest, the specific objectives will be trained for.

The big difference would be after the landings: the US forces get into the grinder at Caen, while the British at the breakout and Falaise gap. And obviously after that the US forces subsequently head north towards Belgium, the Netherlands and the north of Germany, while the British towards the east of France, the Ruhr and the south of Germany. This also would mean that after the war they get different occupation zones.

I wonder what would happen to Market Garden? Would it be performed by the US ground forces, or will Montgomery push for something else which involves the British forces?
he big difference would be after the landings: the US forces get into the grinder at Caen, while the British at the breakout and Falaise gap
Or the US take Caen on D+1, and Brits don't get hung up in the Hedgerows as much, with Funnies with modified Bullshorn plows quickly deployed.
ATL July is a bad time for the Germans across the board.