I don't know of an objective measurement to determine how cruel or harmful a society is. In Asia, syncretism between religions and multi-religion societies were more common than in the west, making it difficult to define what a "Buddhist society" is. For example, Kublai Khan was interested in Buddhism, had a Buddhist monk in his entourage, and forced some Daoist temples to convert to Buddhism. Yet the society he ruled over had Daoists, Buddhists, small minority of Christians, Confucian influence, etc. Would you describe it as a Buddhist society overall?

My knowledge is in Japanese history. Buddhism came to Japan in the Askusa period (510-710). Towards end of this period Buddhism became popular among ruling elites and increasingly integrated into official state functions. By the Nara period (710-794) Buddhism was fully integrated into the apparatus of state power. Japan also had native animist religious practices called Shinto, and these came to function syncretically with Buddhism. Buddhism was associated with Japanese elite society in various ways for nearly a thousand years, and only began to decline during the start of the Meiji period, where the emperor was restored to power. At this time Buddhism was seen as "backwards" for its association with the Shogunate, and Shinto practices were promoted because of the more central place of the Emperor compared to Buddhism.

In the period of Buddhist dominance of Japan was Japan less harmful or cruel than societies in other places? Absolutely not. Japanese society had an extreme social hierarchy with those in power (nobles, royals, samurai) had power and wealth, while those at the bottom had little rights and hard lives. In fact it was during the era of Buddhist dominance in Japan that the samurai class came to power in the late Heian and Kamakura periods. This group gained political power because they were the best at fighting and killing people. Within this 1000 year timeframe of Buddhism prominence in Japan there were frequent internal wars and occasional external invasions. Buddhist groups themselves even had militarized monk orders which fought which each other and samurai. There was the extermination of the Emishi, a separate ethnic group with lived in Honshu. In addition there was ethnic cleansing and persecution of the Ainu people of Hokkaido. Women in Japan were unequally with fewer rights and power than men. In fact, the freedom of women actually declined somewhat from the Heian era compared with the Tokugawa era (for reasons unrelated to Buddhism). I've summarized 1000 years of complex history into a paragraph in the interest of readability and brevity, so let me know if you are more interested in expanding on a specific point.

This is all to say that at least in the case of Japan, a Buddhist society is comparable to Christian Europe for the amount of cruelty and harm it caused.

Sources: William E. Deal and Brian Ruppert, A Cultural History of Japanese Buddhism

Zen at War by Brian Victoria

Edit: I used the word "expertise" to describe my knowledge of Japanese history. I don't think that's a good word to use in this forum where actual PhD's and historians answer sometimes. My BA is history with a specialty in Japanese history, I've lived in Japan and studied its history further on my own. So more knowledge than a layperson, but I'm hesitant to use the word "expertise"

Before you attempt to debate the accuracy of this statement by Russell by comparing body counts, you should first understand what he meant by “the least harmful and the least cruel” within the context of the complete text. Russell’s 1921 lecture “The Essence and Effect of Religion” (delivered at the National University of Peking and first published in the journal Young China) attempted to address two questions:

first, what is the essence of religion; and second, is it necessary to preserve this essence?

Russell’s aim in this lecture was to examine the history and nature of religion to determine which aspects of traditional belief, if any, should be preserved in a secular society, and how ethics and morality can be extricated from religious dogma. As a humanist, Russell was willing to accommodate personal beliefs to a degree as well as what he perceived as benign “primitive” or “native” religious systems. His ire was directed at what he termed “public” religion, especially when it was used a cudgel.

If you look at the context for this quote as well as at the references to Buddhism in his other writings, it’s clear what Russell means by “the least harmful and the least cruel” is what he sees as a relative lack of persecution by those professing Buddhist beliefs when compared to what he considered to be the other “Great Religions” of Christianity, Islam, and Marxism. By persecution, Russell means the use of religion by the state to perpetrate violence against non-believers. He is in no way claiming that nations or societies with a majority or plurality of adherents to Buddhism are more peaceful or that Buddhists are less likely to wage war.

Russell’s statement is meant as faint praise of Buddhism’s willingness to accept a diversity of belief and its apparent lack of dogma. His appreciation of the religious pluralism he perceives in countries where Buddhism predominates is in support of his own philosophical and pacifistic aims and is not intended as an endorsement, as is made clear in the next sentence of the text:

But I cannot say that Buddhism is positively good, nor would I wish to have it spread all over the world and believed by everyone.

SOURCE:

Russell, Bertrand, et al. Russell on Religion: Selections From the Writings of Bertrand Russell. London: Routledge, 1999.

See also this older answer by /u/JimeDorje