It comes across as being like introducing the idea of a contest because which one is more well-known is irrelevant to the question of why an important figure in an important event to both U.S. and British history is only widely-known to Americans.
False logic. The relationship that exists today is a direct result of events hundreds of years ago; ergo, both are important. Saying that the relationship that exists today is important but not the events of the 18th Century is like saying that it's the cake that matters, not the ingredients.
From memory back in the late 18th century early 19th century, the US was far closer to France than it was to the UK.
I mean, sort-of. Obviously we hugged France close during the Revolution, but by the 1790s, the United States was divided between factions that favored closer ties with Britain and factions that favored closer ties with France, and public opinion was majorly divided over whether or not to support the French Revolution. We ended up in a state of undeclared hostilities with the French Republic in 1798 that was called the
Quasi-War, and U.S. foreign policy for a long time thereafter was basically all about which superpower, France or Britain, to support at any given time.
Anglo-American relations improved far more in the last 150 or so years. Espically in the 20th century.
It was really World War I when U.S.-U.K. relations finally turned from the old hostilities of the Revolution and the War of 1812, but even during the inter-war period, there was a lot of suspicion of the Britons -- to the point where the U.S. even had war plans for how to invade and occupy Canada if a war between the U.S. and U.K. broke out. It wasn't until World War II that the U.S.-U.K. alliance was truly solidified the way it is today. But U.S.-French relations have always been weird, and have never been as close as the modern U.S.-U.K. relationship.
Whilst the events where important, different sides place different empathise on certain battles/people. So whilst the US might consider Arnold an important person it does not hold true the UK would.
I'm sorry, but it's just not reasonable to say that Benedict Arnold was not an important figure in the American War of Independence. One might argue that he's not AS important as Americans tend to think he is, and one might argue that the American Revolutionary War is not as important to British history as Americans think it ought to be seen as being, but to say that Benedict Arnold was not important at all is just flat-out nonsense.