Starting with the easy part; Goodwood. The Centurian would have made no difference to the outcome. Monty's plan for that operation, like every major offensive he undertook on the continent was a set piece one to occur on a narrow front. Goodwood faced bigger problems due to its narrow frontage of operations that put alot of pressure on the British to maintain their flanks against counterattacks as they advanced. This in turn greatly weakened the number of available troops to continue to push forward into the German lines.
In such a setting any tank would have been in trouble.

In tank-on-tank operations:

Against the Panther the Centurian would have had an advantage. The Panther is extremely vulnerable from the flank and rear. With its slower turret traverse it is also likely not to be first on target much of the time.

Against a Tiger I the two are more evenly matched with a slight advantage to the Centurian.

Against a Tiger II the Centurian on the offensive would be at a disadvantage while it would have the advantage on the defense.

That's the short version.