"Better" would depend highly on the social standing of the slave, how they were acquired, and what their jobs were. It also depended on the time frame. During the imperial period especially, slaves slowly accrued more and more rights.

For a farmhand or mining slave in the late republic it would be hard for a slave to tell a significant difference between their lot and that of a black slave in Alabama 1855. Their masters could treat them any way they wanted, including physical punishment, or even killing. And they had no legal recourse against it, or any rights in particular. This kind of physical labor was the dominant form of slavery in the late republic especially as the large latifundias developed.

However for a slave that had useful skills life could be very different. A literate Greek man who had been enslaved as a prisoner of war wasn't likely to end up working in a field. He was likely to end up as a clerk or a tutor to his master's sons. He might be granted the privilege of earning money and eventually buying his own freedom. Or after a period of service he may be straight up granted his freedom. Such a man could have a decently comfortable life as a slave, and a hope for freedom and prosperity afterwards. He might not have any more actual rights than a field slave, but in practice cultural norms did grant him more theoretical protections.

Once freed a former slave had limited rights, they couldn't hold public office for example. But there was a degree of social advancement possible and the status of a freed slave only lasted a single generation, the son of a freed slave could hold office, if otherwise qualified. This was no doubt, at least in part, due to the fact that slavery wasn't racially based. Slaves could be former Romans, Latins, Italians, Greeks, Africans, Celts... etc. There was no immediate way to distinguish between slave or free based solely on ethnic features.

Up until now I've focused largely on men. Women slaves were dealing with a lot of the same issues, with the added concern of also being used sexually. In fact a lot of women slaves were used as prostitutes and the brothels were full of slaves. Even an otherwise well treated house servant was at her master's pleasure. But those who were well placed, could also hope to earn their freedom, and eventual respectability for their descendants.

So I guess the TLDR for all of this is, it depends on the individual slave. At the worst a Roman slave could be absolutely as mistreated as the worst off antebellum slave. At the best, a Roman slave could be and often were much "better" treated than in the South.

One key differentiation is that US slavery was race-based, it was ethnic. To the Romans, slavery was a (possibly) temporal status that could affect anyone, even fellow Latins.

To add some details to /u/QuickSpore's post, the more contact a slave had with the master meant the better chance to build a connection and hence better treatment. But those working on a villa with an abentee landlord would have no such tie to their owner and would be mere chattel. However masters recognized that slave's were valuable equipment and not to be written off lightly. Barring periods of intense warfare (which produced an abundance of cheap slaves), slaves were an expensive commodity. So it was in the owner's interest to ensure his slaves were fed sufficiently to allow them to work and kept in good health. These anonymous rural slaves would likely be incentivized mostly through physical punishment of varying means but again it was in the owner's interest to avoid permanently damaging his 'equipment'. Again there wasn't the racial element as these slaves could come from a wide geographical area, of varying races, some even being Italian-born products of other slaves.

For domestics, the daily contact with their masters allowed a relationship to build up which would humanize them more and (hopefully) lead to better treatment. Physical punishments could be used to enforce discipline but more likely it was the hope of manumission dangled in front of each slave that kept them in line. My prof described this as essentially a lottery that each slave could partake in for good conduct.

There was no racial element, as mentioned, because so many slaves were fellow Italians (or even Roman) and so many free Romans had descended from freedmen that making it a racial trait was impossible.