The (heavily nationalist) Irish history curriculum treats the American Revolution only briefly, and puts it squarely in an international context as the beginning of an 'age of Revolutions' in the late 18th century, culminating in the failed 1798 and 1803 Irish rebellions. The focus is very much on the international dimension, including French involvement and the knock-on effects leading to the French Revolution, which is covered in much more detail. The actual details of the American Rev are very minimal - not much more that an overview of the 13 colonies -> their grievances ('No taxation without representation') -> the Boston Tea Party -> George Washington -> Constitution. That's about it.

British history lesson focus on the geographic island of Britain itself, not the wider British Empire or the people affected by it. Even though there were British political actors at the American Revolution it is seen as part of American history because it happened in North America. The Opium Wars are seen as part Chinese history for the same reason. Even 1916 Easter Uprising is seen Irish history not British despite it happening in what was then the UK itself, lead directly to a member state (kingdom?) leaving the Union and having political repercussions into the modern day.

I've just dug out my Spanish history textbooks. One course was of world history, and there is indeed a (short) section about the Independence of the United States.

Not unlike the Irish case mentioned by Miles_Sine_Castrum, it is considered part of a series of revolutions that brought an end to the Ancien Régime in the West. Literally, "it was the first example of burgeois revolution". The Boston Tea Party, Saratoga and Yorktown are mentioned, but in general the textbook is far more interested in the economic and social causes behind the war, as well as the political impact of the Declaration of Independence, the American Constitution and the federal state.

Ironically enough, Spanish contribution to the war is barely mentioned. In other courses, centered around Spanish history, the war doesn't even appear.

The textbook is Historia del mundo contemporáneo, by Alfredo Pastor Ugena, from the publisher Editex (Madrid, 2002).

I'd first like to link to this thread, which asks a similar, but not identical question: https://www.reddit.com/r/AskHistorians/comments/4e9fft/british_historians_how_is_the_american_revolution/

Secondly, here is a google books preview of the main textbook used by (the small number of) British students who study the American Revolution: https://books.google.co.uk/books?id=rI65BwAAQBAJ&pg=PT1&lpg=PT1&dq=The+American+Revolution+and++the+Birth+of+the+USA+1740-+1801,++Farmer++,Hodder+.&source=bl&ots=Gi3XVgEajy&sig=689CxhCM-ESSR7_4KCSEJrJCCho&hl=en&sa=X&ved=0ahUKEwjLjsSH-sjPAhVpJ8AKHW_5Ak0Q6AEIOjAF#v=onepage&q=The%20American%20Revolution%20and%20%20the%20Birth%20of%20the%20USA%201740-%201801%2C%20%20Farmer%20%20%2CHodder%20.&f=false I can't compare it to an American textbook, but presumably you can.

To summarise the first link, the main thing to understand is that for British students, the American Revolution is an optional (for the school) module in the world history section, which is about a third of a 2 year (either 14-16 or 16-18) course. An optional course, since History is not compulsory from 14 onwards. So, if you choose History, and if the school chooses the American Revolution (out of quite a large set of options, everything from the Mongols to the rise of Islam to African kingdoms to Napoleon to the Bolsheviks, etc, etc, etc) as their world history module, you will study it perhaps once a week for a year. There's a very small possibility you will study it for 2 years (if you do it at 14-16 and 16-18, but bear in mind that 16-18 year olds in Britain only study 3-4 subjects so most don't study History. Though if they do study History they'll do each module twice a week rather than once).

So, while this is not directly answering your question, the first point I want to make is that very, very few British students study the American revolution in school. Frankly, we have far too much history of our own to have much time to study foreign history, and when we do, it tends to be Nazis, Communists or the British Empire's actions in other countries.

It's also important to note that most British history (both the history you learn at school, and also the works of important historians) don't focus on the American Revolution as being particularly important to Britain's development, besides reinforcing it's focus on India. Political and Marxist historians, for example, tend to focus on the French Revolution as being much more influential on British politics than the American one.

(Personally, I studied the American Revolution for half an hour in university. It was a lot less interesting than the previous half an hour on Native Americans, but I did learn that Britain cancelled some taxes after America complained, that anti-Catholicism was a factor in the Revolution, and that a third of Americans supported Britain, none of which I'd learnt from American TV)

If you don't want to look through the text book, here is the course synopsis for the A-level (16-18) module: http://social.ocr.org.uk/files/ocr/Y212%20SoW%20The%20American%20Revolution.pdf

And also an example exam: http://www.ocr.org.uk/Images/170551-unit-h105-y242-the-american-revolution-1740-1796-sample-assessment-material.pdf I think the way it's marked is indicative of the way it's taught.

For example, for the question "To what extent were political grievances the main reason for growing hostility to British rule by 1776?", students can talk about political grievances, tax, coercive actions like the Intolerable Acts, events like the Boston Massacre, anti-Catholicism, or the influence of key figures like Jefferson and Adams.

For the question "‘British weakness was the main reason for American victory in the War of Independence.’ How far do you agree?", students can talk about British military weaknesses and the challenge of crushing a distant rebellion, British supply problems, the changing extent of American support for the British, the power of the French, the entry of the Dutch and Spanish, the influence of key figures like Washington, or the development of the Continental Army and military turning points like Monmouth and Yorktown.

Now, I haven't read any American textbooks about the Revolution, so I don't know if Americans are trying to teach their students different answers, but presumably you can compare it. I'll be honest, my assumption is that American textbooks gloss over anti-Catholicism, the importance of the Dutch, Spanish and French, and the Americans who fought for Britain, and focus more on key figures. But this is an assumption I've picked up from how American history is presented in American popular media, which may not at all be how it's presented in History classes.

Something else to note: the main textbook for this course is a specific one for the course, but the three suggested supplementary books include a concise book written by a British university vice-chancellor, a fairly typical one written by an American, and another written by an American that focuses on "non-Anglocentric approaches to American history", with more emphasis on the influence of the Spanish, French, Russians, etc.