Your idea that wage labor would work harder than enslaved labor is an old one. Even before wage labor was the dominant system in Europe or North America, a school of thought held that without incentive to strive on their own behalf and for their own reward, enslaved people just would not perform as well as people working for money or their own subsistence. This was an article of faith among antislavery Americans and a few generations of historians of slavery agreed with them. We mostly don't think that's so anymore, at least as something inherent in the system. Individuals can vary, of course, but neglecting that there are many reasons to be less confident about who works hardest.

Let's start with the conceptual problem. Traditional estimates of unproductive slave labor tend to run from Econ 101 first principles. Enslaved people don't have the incentives so they don't deliver. This neglects that enslavers have a lot of really powerful incentives which are usually not available or not as available to bosses paying wages. Nineteenth century working conditions can get pretty hairy, but they still fall well short of literal slavery. They include actual torture, chiefly in the form of whipping but there are many other forms of violence that one increasingly cannot do to a white person. In some cases they're legally not possible and in others social mores prohibit them. You can't sell a white person's kids or spouse away from them any more than, usually, you can whip them. White laborers can quit and if your reputation gets around you may have trouble getting replacements, whereas enslaved people are stuck. Avoiding all of these, enslaving people grants the enslaver tools that a boss of free labor simply lacks and they are not shy about putting those tools to use.

That doesn't mean that the enslaved don't fight back with the few tools they have, though. Plantation records, enslaver-to-enslaver advice, and nineteenth century racial theory, are replete with references to how the enslaved are lazy, easily confused, or outright incompetent at basic tasks. For all of these, we need to read in intention. Enslaved people vary as much in their skills and abilities as anyone else because they're people, including their inclination to fight back against mistreatment. An enslaved person reported as breaking a tool because of incompetence or carelessness might have actually done so on those grounds, but it happened often enough that enslavers split between investing in harder-to-break implements and switching to really cheap stuff that was easy to replace as a general thing. Likewise they believed that their human property required close supervision in ways that whites did not, to keep them working diligently. The constant stream of instructions misunderstood were, for the most part, probably misunderstood on purpose. Every time an enslaved person does that, they claim back a tiny sliver of control over their own lives and time.

Which points us to the larger issue. Traditional studies of enslaved labor tended to focus on its productivity. In other words, they approach it from the enslaver's POV and ask how well slavery delivered for them. That's an important question -they mostly did pretty well, which is why they kept at it- but it's only half the story. Productivity matters a whole lot to the enslavers, but doesn't matter at all to the enslaved until they're tortured into it.

So let's flip the perspective. Enslaved people and free labor can both have it rough, but the enslaved have it rough on a whole new level. Details vary a lot here, by period, time of year, typical duties, geography, etc. Enslaved people on sugar plantations during planting can expect to be up for 24 hour stretches, using machetes and spending a lot of time in the company of boiling vats. They'll be coerced to work fast in that environment. That's one hard day...or more. Sugar is the main crop grown by enslaved labor in the Caribbean, though not the only one.

Cotton is its mainland North American equivalent. Cotton harvests operate under what's called the pushing system. Each enslaved person has to keep up with a gang working the rows or risk punishment. They're engaged in a backbreaking harvest all day long. It ends with them taking their bags to be weighed and their totals are noted. Your total on your first day as a full hand in the field becomes your minimum. Go below that and you're in for punishment unless, and often even if, you have a really good reason. Punishment in either case is usually measured in stripes on one's back.

But let's set harvest aside for a moment. The enslaved are expected to provide much of their own food. Slave rations, bar times when they need to physically be at 100% (mostly harvests) are usually below what you need to keep going through a day of heavy physical labor. To supplement diets, enslaved people are usually granted plots which they can use to grow their own food, raise stock, etc. But they have to do it on their own time, which is usually one day a week (Sunday), maybe half of Saturday if they're lucky, plus whatever labor you can get done after the sun sets before you fall asleep. That's also family time, time to maintain or repair the shack the enslaved live in, and so forth.

That all sounds like incredibly hard work to me.

Labor is labor and everyone's going to have a rough time of it, but few whites who underperform are going to get whipped or have their kids stolen from them. In terms of enduring physical abuse and exhausting toil, it's hard to imagine a scenario where the average free laborer would look at the average slave and think they've got it easier. This was the fear that underlay a lot of the assertions that free labor was just better: the real prospect that it literally could not compete and either free men would be forced out of the job market entirely -this is an issue in the late antebellum South- or free men would be driven down to the level of slavery -a prospect embraced by one very radical proslavery theorist- as a result of competition.

These concerns point us in uncomfortable directions. We tend to associate productivity and economic dynamism with progress. We then tag those qualities to ourselves. This has led some scholars to believe slavery fundamentally backwards and an economic dead end, essentially other and a kind of historical cul-de-sac which we can safely neglect in understanding the wider contemporary world. But closer examinations of the US Southern economy have indicated anything but. It's certainly reasonable to say that that region, or the British Caribbean, are differently modern from the cotton mills in Liverpool or Lowell, but it's clearly not home to a system which is moribund and, as often not-so-silently implied in the past, on the way to solving itself.