I've read a fair bit into the very brutal fighting around Caen and the grinding attrition inflicted and taken by the Allies during these operations. Reminiscent in some senses of the Eastern Front what with the long sightlines and open fields. I've also just picked up generally that the US had some difficulty in the hedgerows to the south east until new tactics and equipment like the hedge cutter attachment were developed and utilized.

How would the respective western allies fare if their environments were switched? If the US forces had the area around Caen and the Commonwealth forces had the more hedgerow infested area?

I suspect that the 'funnies' such as the Churchill Crocodile and the Churchill AVRE, as well as the WASP carrier (Flamethrower Universal Carrier) would have been very popular in the closer ranged environment of the hedgerows.

Would the US, facing the longer sightlines and ranges in the north thus need the 76mm Shermans sooner?

I predict the Commonwealth forces would perform not as well, due to their inability to as effectively wield their artillery based strength, while also being particularly vulnerable to infantry losses, a notorious bug-bear for the Commonwealth based forces at this stage and ongoing of the war.