It is unfortunate that Kropotkin's intellectual descendants, the anarcho-communists, rejected the strongest part of Bakunin's analysis, the anti-statism, and emphasized the weakest part, poor economics and self-immolating altruism in the name of "humanity." Kropotkin stressed this altruism, writing extensively about "mutual aid," but interpreted it as a negative-sum game. In other words, he saw mutual aid as non-profit selfless altruism; he seemed to have no clue about the insight of the individual anarchists - that social interaction could be a win-win situation. The modern notion of free markets, and trade being beneficial ex ante to both parties in a transaction, while understood by Warren, Spooner, and Tucker, were apparently beyond the pale of Prince Kropotkin.
Kropotkin was one of the originators of the mistaken notion that anarchism opposes social hierarchies of all types, rather than only imposed, coercive hierarchies. This rejection of voluntary leadership and natural hierarchies have continued to this day, much like the terrorism of "propaganda of the deed," in giving anarchism a bad name.
That is why Anarchy, when it works to destroy authority in all its aspects, when it demands the abrogation of laws and the abolition of the mechanism that serves to impose them, when it refuses all hierarchical organization and preaches free agreement - at the same time strives to maintain and enlarge the precious kernel of social customs without which no human or animal society can exist. - Peter Kropotkin, Anarchism: Its Philosophy and Ideal (1896)
Another idiosyncrasy of Kropotkin was his idealization of the mir - the russian peasant village society. In this regard, he anticipated the late 20th century anarcho-primitivists. While Kropotkin was so conservative and reactionary as to want to return to pre-feudal agrarianism, primitivists want to go back even farther - to hunter-gatherer days. These anarcho-primitivists apparently don't know (or don't care) that the objective conditions for the hunter-gatherer lifestyle required human populations to be as sparse as the bear population. To return to such a society would require the elimination of over 98% of humanity. While this could happen by nuclear or biological apocalypse, this does not seem a reasonable basis for social activism!