What fundamental differences in ideals separated the American colonies from Great Britain after 1763?
Actually, there was not a great deal of difference between American and British ideals. Almost all Americans prior to the revolution considered themselves the King's good and loyal servants and were proud of their English heritage. The most precious of these was their "rights as Englishmen."
After the Seven Years War when Parliament attempted to tax the colonies for the expense of defending them, the colonists insisted that they had been denied their rights as Englishment. Even after Lexington and Concord, an Olive Branch Petition was sent to George III offering to call off hostilities if they could only be granted their rights as Englishmen:
The apprehension of being degraded into a state of servitude from the preeminent rank of English freemen, while our minds retain the strongest love of liberty, and clearly foresee the miseries preparing for us and our posterity, excites emotions in our breasts which, though we cannot describe, we should not wish to conceal. Feeling as men, and thinking as subjects, in the manner we do, silence would be disloyalty. By giving this faithful information, we do all in our power to promote the great objects of your royal cares, the tranquility of your government and the welfare of your people.
We ask but for peace, liberty, and safety. We wish not a diminution of the prerogative, nor do we solicit the grant of any new right in our favor. Your royal authority over us, and our connection with Great Britain, we shall always carefully and zealously endeavor to support and maintain.
George III refused to even read the petition. It was only after this, that Thomas Paine wrote Common sense in which he argued that the King (and Parliament) were responsible for the war; and that the Americans had evolved into a separate nation who could no longer be part of the British Empire:
Every thing that is right or natural pleads for separation. The blood of the slain, the weeping voice of nature cries, 'tis time to part. Even the distance at which the Almighty hath placed England and America, is a strong and natural proof, that the authority of the one, over the other, was never the design of Heaven.
There is some argument that during and after the Seven Years War, Americans developed a separate identity as such. Still American ideals and British ideals were not that different.
The main difference in ideals between the colonies and the mother country was that the colonies had evolved a set of ideals that were built more around freedom and individual rights than the British ideals, which were built more around respect for authority and tradition. This difference can be seen in many different ways.
For example, the difference showed up in politics. In America, there was no desire to have a nobility that had a part in politics. Instead, there was more of a move towards (though not all the way to) the idea that all white men should participate in government. As another example, economic activity in the colonies was much less regulated than it was in England. It was much less tied up by rules created by guilds and upheld by tradition.
In these ways, the ideals of the colonies had moved towards individualism and away from traditional deference to authority as was more common in England.