Short answer? No.

Long answer? It depends on what you mean by "brother".

Up until shots were fired on April 19, 1775, most Americans believed themselves to still be loyal subjects of England (there was a strong movement in rural Massachusetts towards independence in 1775, but they were quite radical and were viewed that way).

Even after fighting began there was still a strong feeling among many Americans to seek reconciliation. So in that sense, the entire war was of Englishman vs Englishman.

However I suspect that you're not really asking about that, but more specifically about American colonist vs American colonist.

There was a very strong element of civil war to the Revolutionary War. Nearly every engagement fought in the Revolutionary War had Loyalist militia in one role or another. There were nearly 400 engagements in the war that were just American militia units vs Loyalist militia units (with no regulars from either side).

In fact, during the course of the war there would be more than 200 Loyalist militia units formed. Some of them would only last a few months, some would last the course of the war. This also doesn't consider the number of men who fought as privateers, who joined the British Army as regulars, or who joined the Royal Navy.

This militia vs militia aspect was perhaps most visible in New York and New Jersey, and in North and South Carolina, but there were elements of it in nearly every state.

The Revolutionary War divided families. Henry Knox's in-laws were strong Loyalists. Two of his brothers-in-law actually served as officers in the British Army.

Benjamin Franklin's son William was another strong Loyalist and actually served as royal governor of New Jersey.

Samuel Prescott (one of the commanders at Bunker Hill), had a brother-in-law that was a strong Loyalist. Timothy Pickering Jr (who was a general in Washington's army) had a father who was a Loyalist.

In 1781 Nathanael Greene wrote to Washington and said this about the war in the Carolinas:

"The division among the people is much greater than I imagined and the Whigs and Tories persecute each other, with little less than savage fury. There is nothing but murders and devastation in every quarter"

The sheer number of Loyalists who left America after the war indicates the divided nature of the country. After William Howe abandoned Boston in 1776, 1100 Loyalists left the city with him and sailed to Nova Scotia.

At the end of the war at least 80,000 Loyalists left America in a mass exodus (some historians put the number as high as 100,000). There were thousands who left for England or Canada during the course of the war, and of course there were thousands who had died.

So yes, the Revolutionary War was very much a war of divided loyalties and split communities.

Very interesting question, but unfortunately, I do not think anyone can say it this contention is totally true or completely false. This is a complex issue with a ton of caveats about the time, place, and context of families being on opposite sides of either conflict. I will direct my answer at three central points that may help clarify: First, that the "brother vs. brother" mythos of the American Civil War is partially, if not largely, a purposefully constructed memory of the post-war era (specifically 1880s and 1890s). Second, that there is historically proof of family members participating on opposite sides of the Civil War, though in smaller numbers than the myth suggests. Third, that the revolutionary war (at least according to a few historians) was more of a inter-family conflict that it has traditionally been credited with.

During the Reconstruction era, Northerners and Southerners began the process of memory creation, focusing on the sacrifices their men, women, cities, and regions gave during the war. This memory creation and corresponding historiography would evolve several times over the following century. During and immediately after Reconstruction, generally speaking, history was told from the top down, as a story of great men and great deeds. This trend was soon overtaken with a penchant for memorializing the sacrifices of the citizens and soldiers who fought the war, but still told in a very top down fashion. As this trend evolved, both northern and southern veterans (and their families) began to memorialize the war as a family quarrel, a disagreement between brothers, where both sides fought honorably and had a legitimate cause. I am obviously giving an overview of this process, as it is intricately complex. The point to take away is that this process of memory creation, though maybe not explicit in the minds of both sides, was at least part of the motivation to publicize the "brother against brother" aspect of the conflict. (Sources: David W. Blight, Race and Reunion: The Civil War in American Memory; Eric Foner, A Short History of Reconstruction; Barbara Gannon, The Won Cause: The Won Cause: Black and White Comradeship in the Grand Army of the Republic; Gary W. Gallagher and Alan T. Nolan (ed.), The Myth of the Lost Cause and Civil War History; William C. Davis The Cause Lost: Myths and Realities of the Confederacy).

Now, we have established that memory construction influenced the stories that both sides liked to highlight in their telling of Civil War history. But was there proof of brother fighting brother? Well, yes. Lincoln's extended family (through his wife Mary Todd) were slave owners and several fought for the South. Grant's wife's family owned slaves and fought for the Confederacy, as well as a few other prominent individuals that I will not bother to go into here. What is more fascinating (in my opinion) is how antebellum economies, societies, and polities influenced the family emigration to various states or territories for various reasons. In St. Augustine FL. for example, many people of northern birth resided in the town, some of whom fled North at the beginning of the war, while others stayed and actively supported Florida's war effort. Though this was not a statistically large group, you see similar trends across the South. Transplanted northerners (and southerners for that matter) either adopted their new state's allegiance or went on to support their old state's cause. Again, these stories are always widely espoused and highlighted by late 19th and early 20th century historians as examples of this family feud telling of Civil War history. However, to my knowledge, there does not exist a thorough treatment as to the numbers of family members--extended or immediate--who faced each other in this war (Sources: Amy Murrell Taylor, The Divided Family in Civil War America; Thomas Graham, The Awakening of St. Augustine: The Anderson Family and the Oldest City, 1821–1924).

So if the Civil War could not be necessarily described as a "brother vs. brother" war, can we say that the Revolution was? A few historians would say, yes. The Revolution was fought largely by small and deeply divided communities. Across the colonies, there remained substantial amounts of loyalists or neutrals who did not support Patriot forces. Historians like Hull would state that support for the Revolution (which ebbed and flowed based on contemporary events, as with all wars) could be considered as little a third of a communities population, with another third representing loyalists and the last group remaining neutrals. It is also important to point out that certain whole communities were neutral, see the Quakers. So, depending on the time and place, various communities were deeply divided by the war and it was common to see families broken apart by such division. Though I decried it above, there are famous examples of these divisions, such as Ben Franklin and his son, who were on opposite sides of the conflict. But again, because of the large amount of loyalists who fled the colonies after the war, it is hard to get a firm statistical number of how widespread these divisions were. (Sources: N. E. H. Hull,Peter C. Hoffer and Steven L. Allen, "Choosing Sides: A Quantitative Study of the Personality Determinants of Loyalist and Revolutionary Political Affiliation in New York," Journal of American History, Vol. 65, No. 2 (Sept. 1978), pp. 344-366; Thomas B. Allen Tories: Fighting for the King in America's First Civil War; Joseph S. Tiedemann, The Other Loyalists: Ordinary People, Royalism, and the Revolution in the Middle Colonies, 1763-1787; Ruma Chopra Choosing Sides: Loyalists in Revolutionary America).

So, to sum up, the "brothers vs. brothers" mythos of the Civil War is largely a purposefully constructed memory that meant to enshrine the shared ideals of mutual sacrifice of white veterans and their families during the 1880s and 1890s. Though there are instances of families on opposite sides of the war, these are widely publicized and may not be as common as previous histories would contend. Lastly, the American Revolution--because of the way that communities north and south were internally divided over loyalty to king and country--has been argued to be a true "brother vs. brother" conflict, more so than the Civil War. However, with both cases, there remains no definitive work or statistical analysis of these points, though small case studies exist to contradicting findings. Thanks to everyone who contributed.