Why isn't slavery in Britain/British empire talked about as much as slavery in the USA?

Well, the first thing to keep in mind is that you have to distinguish between popular culture and the actual study of history. In academic circles, a great deal has been written and said about slavery in the British Empire. There is an absolutely enormous body of scholarship on slavery as it was practised in the British Caribbean; and of course, you cannot neatly separate out slavery in the United States from slavery in the wider British Empire because although they had evolved into divergent systems by the antebellum period, US slavery of course begins with the use of slave labour in British colonies decades before American independence. So slavery in the British Empire certainly isn't a neglected field of study. Nor is it without strong cultural representation in the United Kingdom; the slave trade is fairly popular option for study in British secondary schooling curriculum, and the International Slavery Museum is based in Britain and looks at slavery from a much broader perspective.

You are certainly right though that in popular culture, slavery in the United States is much more widely represented and discussed than slavery in the British Caribbean or in the pre-independence colonies. Within the United States, this much is to be expected - throughout the western world, we tend to teach history in very nation-specific contexts. There is an expectation that history in compulsory schooling should be about the history of your own nation, and even when we teach children about the history of other countries, it is usually to help them understand events that have significance for our own history. Americans, then, are going to be most familiar culturally with their own historical experiences with slavery - and American popular culture is ubiquitous around the world thanks to that nation's enormous economic power and political influence.

As /u/youngmarshall also rightly observes, slavery's lasting impact on American life has been much more profound and significant than in Britain; there are millions of descendants of black slaves living in the United States today and still suffering for the legacy of slavery, and the nation fought a costly and devastating Civil War over its abolition. You simply cannot escape the day to day legacy of slavery in the modern United States in the same way that you can in the modern-day United Kingdom; whilst slavery in the British Empire was profoundly significant to the story of its economic, social and political history, it did not leave the same kind of deep scars on mainstream British society's collective psyche as it has in the United States.

Britain has also arguably tried to ameliorate the memory of its own involvement in slavery by emphasising the experience of abolition over slavery itself. The abolition of slavery in the British Caribbean coincides with a dramatic shift in British politics towards a political structure that much more closely resembles the modern-day parliamentary democracy of the United Kingdom; it is not uncommon to encounter the notion that slavery and the slave trade were ultimately the responsibility of a narrow elite who were at odds with an ordinary population fiercely opposed to slavery, who reacted against that elite accordingly when the 1832 Reform Act (which expanded the electorate, made district boundaries more representative and led to the first election we can somewhat meaningfully compare modern elections to) allowed it. This is something an over-simplification, but it is not without an element of truth. Likewise, a lot of attention gets focused on the slave trade in British education rather than slavery itself.

But the issue you identify in your question is really a symptom of a much larger problem with popular and even academic conceptions of history; a problem reflected in your choice of question, in fact. Although you have identified that we do prejudice the experience of slavery in the United States over the British Caribbean in western discourse, both are closely intertwined systems with an obvious common ancestry. Both are features of the history of English-speaking North America. Yet when we talk about the experience of transatlantic slavery, it is really Brazil that stands out as the hotbed of New World slavery - not America or the Caribbean. 4.7million men and women were trafficked to Brazil from Africa during the course of the transatlantic slave trade, compared to just 2.7million who went to British North America or the United States. There were vibrant French, Dutch and Spanish slave trades in the Caribbean and Americas, too; and in India and Africa, colonial powers were also using systems of forced labour that could arguably be described as forms of slavery.

So as much as we can speak of an American bias in popular discussions over the slave trade, we can also speak of a kind of anglocentric bias; a disproportionate emphasis on the experiences of the English-speaking Northern hemisphere is placed on these discussions. This is in part explainable by the very obvious cultural impact these powers have had on much of the world (both today and historically) and by the nature of access barriers to scholars; obviously, it's a lot easier for a scholar in New York to read plantation records from the Carolinas than it is for them to go to Brazil and identify records written in Portugese. But it also reflects a western and anglocentric bias that has permeated academic and popular history alike.

Before about the 1980s, academic scholarship broadly tended to be trapped in a notion of the world where all of history is understood with the western world having primacy of agency; in other words, the western powers act, and the rest of the world reacts, as opposed to a view of the world where all states and peoples both act and react on and to each other. Slavery has been studied by academics for decades and decades, but most of the early scholarship is interested in understanding it solely in national contexts. Since the 1970s and especially the 1980s though, scholars have focused more and more on what we can call a kind of global history; histories that try to appreciate historical nuance and refrain from giving the western world, and especially the English-speaking western world, absolute primacy. Likewise, political developments in Spain, Portugal and South and Central America have made historical study on those contexts much more feasible for both home grown and international academics with an interest in those contexts.

In terms of academia, the Caribbean has actually been one of the main beneficiaries of this shift in academic scholarship and historical discourse. Although very much part of the western world, the Caribbean was traditionally seen as being of interest as a periphery to the story of Europe, much like large parts of Africa have been - the history of the British Caribbean was the history of Britain acting in the Caribbean, the history of the French Caribbean was the history of France acting in the Caribbean, and so on. Even after independence swept the region, Caribbean studies struggled for real legitimacy for a time. Since the late 1970s though, scholars like Hilary Beckles, Verene Shepherd, Gad Heuman, Mimi Sheller, Nigel Bolland and so on have really led a dramatic rethinking of the role of the British Caribbean in the world; we can now speak today authentically of histories of the Caribbean peoples, regions and nations in their own right rather than just as extensions of Western Europe, including histories of slavery. That has done a lot to really stimulate more detailed study of slavery in the British Caribbean as a complex and distinct socio-economic system worth understanding in its own right, rather than just as a simple extension of Britain's imperial project. Likewise, there is also more emphasis in scholarship on the very real impact the Caribbean had on Britain and Europe.

Those kind of developments are slow and awkward to move into popular culture and conceptions of slavery, though. Popular histories, particularly those taught in compulsory education, tend to remain very nation-focused; they do not adapt easily to this widespread shift towards more globally inclusive histories. In part, that is an inevitability - there is only so much you can teach in a school curriculum, and any given topic will only attract so much popular interest outside of education. In the United States the history of slavery most people encounter is always going to be American-centric, and with the prominence of American media and culture in the world today, that has ramifications for how transatlantic slavery is discussed globally.

In the case of Britain, British education and popular culture does have a much more British focus (and the emphasis on the slave trade, which was much more of a British than an American phenomenon, reflects that); yet it still very much lacks a focus on the Caribbean, where slavery as a system of labour was actually being used. So whilst Britain of course has its own enormous input into global discourse on the history and legacy of slavery, our domestic cultural focus remains very problematically trapped in this model of Britain acts and the world reacts; outside of the academic world, Caribbean voices - and thus the most significant voice of the experience of African slavery in the British Empire - do not really factor into that representation.