Consider Montaigne's assertion concerning a New World tribe that practices cannibalism: "We may then call these people barbarous, in respect to the rules of reason: but not in respect to ourselves, who in all sorts of barbarity exceed them." Does Montaigne's argument that "civilized" societies exceed simple societies in terms of violence and barbarity still ring true today?

Yes, Montaigne's assertion that so-called "civilized" societies exceed "simpler" societies in terms of barbarity and violence still rings true to today. More powerful societies, as Montaigne understood, are quick to point the condemning finger at the actions of other, "simpler" societies while ignoring or rationalizing the much greater violence of their own way of life. The Amish might have some problems with sexual or physical abuse, for example—and those transgressions are often widely publicized as a great and shocking horror—but the Amish haven't started wars that have cost millions of lives, they don't have nuclear arsenals, and they don't incarcerate a shocking percentage of their population in cage-like prison cells. While we in "civilization" no longer have very many "simpler" societies still existing in the world to compare ourselves to, we also might condemn the remnants of Stone Age tribes in the Amazon who ritually club each other over the head and say that is terrible, while at the same time we engage in more brutal fraternity hazing and army training rituals, not to mention torture and waterboarding of suspected terrorists. Montaigne is right that "civilized" societies need to examine their own high levels of violence and barbarity. It is too easy for these practices to become "business as usual" that we have feel we have no choice about.

The response to this question depends on opinion and I will offer two possible responses to the question.
Presumably, when one talks about "simple societies" we are talking about those that rely mostly on nature and that have little use or awareness of technology—not unlike the "cannibals" that European explorers encountered in the fifteenth-century who had never seen a gun before. Currently, such societies might include the Masai in Kenya and Tanzania, the Yanomami in the Amazon, and even the Amish in Pennsylvania and Ohio.
Some would say that these societies are just as prone to barbarity as more "civilized" societies, just on a smaller scale. For example, in recent years, stories have emerged about sexual assault in Amish communities. Though this was not the kind of barbarity that Montaigne had in mind, 'barbarity' is defined as cruelty or inhumane treatment. Non-Western tribes have also used violence to settle conflicts and have incorporated it into their rituals. Mayan civilization, for example, was remarkably violent. Furthermore, it was a "simpler" society compared to what existed in Europe but a powerful one. Therefore, even in the context of his time, Montaigne's comment did not ring completely true.
Others would say that these "simpler" societies are less prone to barbarity due to their insular habits. There may be occasional intra-tribal or inter-tribal conflicts, but that strife does not cause massive death tolls. Civilized societies communicate with one another, depend on one another, and meddle in the affairs of others, usually to protect interests in resources, such as oil. This tendency to meddle—as well as the need to intervene in perilous situations, such as the rises of Nazism in Germany and a militarist regime in Japan, and the current troubles with the Assad regime in Syria—leads to international war, the ultimate expression of barbarism, considering its death toll and historical impact.