That is a really difficult question.

As an historian, I'm not really in the business of devising that kind of metric. And in the case of human trafficking and bondage, I think there's a moral imperative not to relativise the atrocities suffered by one group by comparing them to those suffered by another. Yes, it is possible to observe differences in the conduct of slavers, slave-owners, &c., but I could never judge which was 'worst' for the victims : the Belgian Congo Free State vs North America vs Brazil vs anything else.

When faced with primary source accounts of slavery and enslavement during this period, my question is how that treatment, that experience compares to the life of someone possessing full personhood and citizenship in that society. Actually, that's one of my first thought experiments when dealing with any differently-privileged group.

Is there a specific aspect or practice of New World slavery that prompted this question?

It's easy to find slavery and forced-labor situations, in history, that were worse than the African-American slave trade in one way or another. The Belgian Congo company, disappointed that the natives weren't savage enough, use bribery and deprivation to create the inter-tribal warfare conditions that are still stirring up genocidal wars in Africa to this day. The Nazi slave-labor camps treated their slaves even worse in terms of food and shelter. I'm sure people will cite other examples.

But the horror of the African-American "triangle" slave trade went on for centuries, and in most places only got worse, not better, as time went on. It's notable for that reason, if no other. Belgian missionaries and journalists were able to shock the conscience of the Belgian people, bringing an end to the worst abuses in a matter of years. The Nazis were conquered and their surviving slaves liberated in about the same amount of time. The degrading treatment of dark-skinned slaves in the New World went on for over three hundred and fifty years. And still has its defenders! That's a kind of horror that can be argued, I think, to be worse than any more intense but more short-lived degradation.

I guess as a related question, and one that the answer to which might answer yours, would be what the mortality rate was for slaves (both in their transfer from Africa to the New World and in the fields themselves) in terms of life expectancy and then compared with other, brutal forms of forced labor.

As a percentage killed over time I have to imagine that Nazi or Soviet labor camps, where killing the inmates was the point of the labor, would be more "brutal and violent" by that metric, but I don't have those figures, and I suppose that might not qualify as "slavery."

Still, I'd be interested to hear from someone who knows more about either

Is there any reason to suspect Southern US slavery was any more violent than, for example, that of Roman gladiatorial slaves?

No, depending on specific types of slaves. During the imperial Roman era, quarry slaves had an estimated life span of seven years, which was "a fair deal longer" than mine slaves (a specific number wasn't given for mine slaves). You can of course talk about the psychological effect and the dehumanizing of an entire race as being "worse." But as far as life expectancy? You were sent to the mines to be worked to death rather quickly. There were slaves that tended to families and farms in the Roman era that were treated better of course, much like the "house slaves" of the New World.

source: Slavery in the Roman Empire. Reginald Barrow.