It certainly shattered the German positions, with many of the German units being not combat effective when the Americans began their assault. However, that very assault was delayed by friendly fire. Instead of bombing parallel to the American/German lines, the bombers had to use a perpendicular approach (the old story was that it was a mistake, more recent arguments that it was a spatial requirement are fairly compelling). As a result, the bombs "crept" toward the American positions. Over a hundred Americans were killed, including the highest ranking American to die in the European theater--Lieutenant General Lesley McNair.

The exact repercussions on later conflicts in Korea and Vietnam is largely outside my research. However, there is definitely an institutional memory of the friendly fire during the bombardment that influenced future usage of level bombers. Improved navigation and bombing accuracy as well as a determination not to hit friendly forces led to the successful use of B-52s in Vietnam during conventional warfare--particularly during the battle of Khe Sanh.

One other note about Cobra--we cannot forget or underestimate the contribution made by the British and Canadians on the left flank. Their Operation Goodwood was an absolute grinder of a battle, and it not only depleted German units in the area but it also drew reinforcements to the fight near Caen that could have been employed against the Americans in Cobra. The hammer blows of Cobra--hard as they were--hit an enemy already weakened by the conflict around Caen.