Johns abuse led to the revolt that produced the Magna Carta.
Georges abuse of the colonies led to the Declaration of Independence.
That's not quite the case.
John was incompetent and a complete failure. All of this was made even more glaring by the fact that he followed two strong and fairly successful kings.
The American colonies had been growing apart from the British since the first colonists came to America. The French and Indian War was extremely expensive and the British thought America should pay for some of it. These abuses eventually resulted in the Revolution; a major factor in the Revolution was George's pride, otherwise it is likely that Parliament would have withdrawn the troops much sooner.
However, the Revolution aside, George III was extremely popular with the British. His reign saw the defeat of Napoleon and solidified Britain's power for the next century. Granted he suffered from dementia, blindness and other ailments in the last decade or so of his reign (during which time his son served as Regent), but he remained popular.
It was during the reign of George III that the British monarchy allowed Parliament to assume ever more control of politics and saw the emergence of a true constitutional monarchy.
The general opinion of Britons today is that George III was incredibly successful. American independence was inevitable at some point and aside from the period surrounding the War of 1812 America has always enjoyed great relations with the UK.
It points to the general failure of analogy, but more relevantly, it shows that drawing historical parallels doesn’t generally work very well. :’) John’s nickname was Lackland — he had problems ruling as a regent, and that got worse when Richard got picked up on priors (/joke alert) by another of the crusader kings while on his way home. John didn’t have a feudal freehold that he could call his own until he got himself crowned, but he wasn’t either a war leader or a strong secular leader, and the barons sensed blood in the water. And of course, the whole feudal ruling class was made up of violent thugs. The only thing that kept them from killing John when they cornered him was, no one much wanted the job, and they’d gotten everything spelled out (they thought) to ensure they wouldn’t have to worry about continuing to enrich themselves and have jousts and extramarital side action and such. And, they weren’t fired up about carting their asses the length of the Mediterranean to fight in the Middle East when they could be enjoying themselves.
In the American colonies, the colonists were *mostly* not aristocrats, or as the old joke goes, impoverished nobility. Some were hired by or otherwise recruited by the various well-borns who had received (for a fee) a charter or license over some often vaguely defined chunk of the eastern seaboard, that had previously no English settlements. Skills that came in handy for 17th c industries — building mills for example, or any kind of skin-handling (furriers, glove-making, etc etc) were bound to produce goods for the British market.
What caused the rupture was the dawning that none of the lands were historically deep feudal possessions. It was freeing, and undermined the feudal basis by which the aristrocratic ruling class continued to run England and its possessions. Chopping out a home of their own, learning its ways (including the ag practices adapted from the non-Euro locals), and making lives for themselves went on for 150 years and more (in my family, six generations, including the first two born in England) throughout the colonies.
The English Civil War, culminating in the beheading of Charles I (an act Cromwell called “a cruel necessity”) had a very real impact on the development of American society before the American Revolution. The Restoration brought back the monarch, but the struggles that had preceded the ECW had shown that political power lay with Parliament. As someone noted in another thread (the one about Prince Andrew), James II was booted from the throne just like that when he tried to restore Roman Catholicism in the UK (more to the point, in the palace). His daughter and her German husband were declared the monarchs. They chased James into exile in France.
Since the ECW, the authority of the British crown has been curtailed, bit by bit (sometimes in bigger bits than in other times); the Parliament has dealt with dynastic failures (James I / VIth was declared monarch upon the death of Elizabeth; Queen Anne died childless and the line of Georges started) by voting. The reality probably is that the American Revolution had some of its roots in the English Civil War, and the erosion of monarchical power through gradual political processes is partially rooted in the American Revolution.