Dammit. I'd written an entire response to this and accidentally deleted it.

Anyway, this is a great question. Tannenbaum's thesis was largely discredited for decades, namely by social historians of the 1970s who saw him as romanticizing Spanish/Portuguese American systems of slavery. However, in recent years some historians have taken to "rescuing" certain aspects of Tannenbaum's thesis.

Foremost among them is Alejandro De la Fuente, who wrote an influential article subtitled "The Tannenbaum Debate Revisited." In it, De la Fuente argues that despite some of Tannenbaum's glaring oversights and exaggerations, his analysis provides some useful frameworks through which to understand the different forms of slavery in the Americas. Namely, unlike the social historians who followed him, Tannenbaum considers how the law in these different societies was influential in the development of their slave regimes. In my notes for that paper, I wrote: "De la Fuente “saves” Tannenbaum only in his analysis of the centrality of legal regimes to slave conditions, not in his linking slavery/law to race relations."

So the question then becomes, were legal regimes really central? Well, De la Fuente makes a convincing argument in favor of this thesis. Slaves in Spanish America, for example, had at their disposal a 13th century legal document (the Siete Partidas) that granted them the inviolable right to, among other things, practice Catholicism and purchase their own freedom. Slaves in Spanish America were also theoretically given legal protection against excessive punishment from their masters, and the state would intervene, in many cases, if the master got out of hand (this, obviously, differed depending on the context). The legal standing of slaves in Spanish America was limited, but they did have legal standing.

Of course, the benefits afforded to slaves as a result of this weren't universal. Slaves in nineteenth century Cuban sugar plantations, for example, had less access to the courts than did their urban counterparts. De la Fuente departs from Tannenbaum's thesis insofar as while Tannenbaum gives the laws themselves social agency (that their existence inherently made the lives of slaves better), De la Fuente argues that the laws were important in how they were integrated into slaves' claims-making.

Some historians are still reluctant to give credibility to Tannenbaum (because of the aforementioned fear of the romanticization of Spanish/Portuguese slavery). However, I find DLF's arguments to be entirely solid. Legal regimes in the different empires were different, and as a result citizenship and legal rights theoretically available to slaves (whether or not they were able to universally access them at all times) produced distinct forms of slave relations across these different contexts. Slaves' ability to make claims gave the state a regulatory power over master-slave relations that simply didn't exist in most British American contexts, even if in some Spanish American contexts it was less relevant than in others. Such an argument doesn't attenuate our condemnation of these slave societies, but it does help contextualize how individuals' lives as slaves were influenced by more than just the social and economic relations that governed their everyday lives. Slaves in Spanish America were able to make claims via the legal system in ways that were inaccessible to their British American counterparts.

I've only begun to scratch the surface on this question, and my answer here's a truncated version of what I originally wrote. But if you have any questions, feel free to let me know. Here's another paper by De la Fuente and Ariela Gross on comparative slave systems in the Americas. Hope this helps!

A lot of what I did for my undergrad thesis dealt with this topic. Tannenbaum argued that there were two key factors that explained why blacks in Latin America appeared to have a better existence than those in the United States; they were Spanish slave law and the role of the Roman Catholic Church. Spanish slave law was based on a slave code called the Siete Partidas or Seven Parts. This law was based on Roman slave law and gave slaves certain protections and paths to freedom. Tannenbaum argued that this legal ability to access freedom made manumission more common so “slavery carried no taint” in Latin America because society was ready for the release of black slaves. This readiness decreased the discrimination levels in twentieth century Latin America.

One legal protection Tannenbaum emphasized was the ability of slaves to testify in Spanish courts. He claimed that since slaves could testify in their own defense, they were able to sometimes defend themselves from the worst abuses of the slave system. This was much different than slavery in the Anglophone colonies where slaves could never testify. Tannenbaum claimed this ability to testify was the key to the alleged superior slave treatment that slaves received in Latin America.

Finally, Tannenbaum claimed that the Roman Catholic Church was able to ameliorate the condition of slaves in Latin America. The Church was able to do this because it was an important part of Spanish colonization. Since one of the goals of Spanish colonialism was to save as many souls as possible, the Church sought to Christianize black slaves. The Church not only thought of the spiritual but cared for the physical well-being of the slaves because they were seen as God’s children. Tannenbaum said the Church played a paternalistic role that few churches attempted to do in the Anglophone colonies and this played a large difference in the treatment of slaves in these two areas.

Two important aspects of Slave and Citizen that distinguished it from later works were the nature of its publication and its use of sources. Tannenbaum published his work with a non-academic press and intended it for a popular audience as a thought-provoking piece on racism during the postwar era. The books that followed Tannenbaum’s on comparative slavery were published largely at academic presses for an academic audience. The other part of Tannenbaum’s work that separated it from later works was he did not use Spanish archival documents and instead used translations of these documents in English. These two differences were part of the criticism of Tannenbaum’s work later on.

The next generation of scholars such as Eugene Genovese observed the civil rights movement and its aftermath during the 1960s and 1970s and asked if outlawing de jure segregation would end racism and when it failed to why was this racism still there? These scholars challenged Tannenbaum on the effectiveness of the law to determine slave treatment and attacked his assertion that Iberoamerica was appreciably less racist than Anglophone America. One of the ways that they criticized Tannenabaum was examining opportunities for slaves after emancipation in Mexico and Peru. These scholars came to the conclusion that opportunities for free blacks were not great in Iberoamerica and as in Anglo-America they still faced discrimination. The failure of the law to improve the lives of many blacks in the US in the post segregation era led scholars of the time to question the law as a way for measuring slave treatment. At the same time, scholars who saw the racial discrimination of the Civil Rights period began to separate race as a separate category from slavery. Eugene Genovese characterized slave treatment as a slave’s living conditions which were equal to their material living conditions, social conditions, and access to freedom. With this formula of sorts, Genovese criticized Tannenbaum’s temporal and geographic vagueness in his work because according to this formula there were even great differences within imperial systems.

During the mid 2000s some scholars took a fresh look at Tannenbaum's arguments and found new value in them. For example, in his reexamination of Tannenbaum’s work for the American Law Review Alejandro de la Fuente acknowledged that although high expressions of the law were not sufficient to understand slaves' everyday lives, they cannot be ignored either. At least part of the power dynamics between masters and slaves and slave agency itself was due to the law where the slaves were. De la Fuente went on to argue that emancipation was more frequent in Iberoamerica because of slave laws there. He went on to use a case study done of Louisiana which showed that manumission rates were highest during Spanish rule in region. While differences in the slave trade are exposed through comparison, commonality is also found in works like David Brion Davis’ Inhuman Bondage where he claimed that all slaves were universally vulnerable to sale, punishment, and death.