Possibly obvious follow-up: Were the two systems really similar? Or have westerners used the term feudalism because it looked like it? Even if they were similar, in what way did they differ from each other?

If by "feudalism" you mean "decentralized monarchy", then the reason for the parallel developments is simply because they (and others) developed under similar circumstances to meet similar needs. The Carolingian breakup and viking raids in Europe, and plummeting tax revenues and frequent local revolts in Japan proved too much for their governments to handle. To keep at least some form of control, their governments legitimized local strongmen to keep order, gave them military and administrative rights in exchange for legitimacy, obedience, and a share of the revenue.

If you go down to the nitty-gritty details, i.e. "Feudalism", with its demesne, homage rituals, rites, and courts, you'll find that a lot of scholars of the Middle Ages in Europe argue that it should be confined to high-medieval France as other places had other different situations and legal background. Kings of Europe also understood very well the systems short-comings, and aimed through various means to centralize control, to varying degrees of success through time. So it was in Japan as periods differ.

We see some similarities. For instance political control was by local hereditary families, centered around manors, castles, or cathedrals/temples. The relationship was seen as reciprocal. If the higher lord does not uphold his end of the bargain in guaranteeing hereditary land rights and offer new rewards, the lower lord would see that he need not meet his military and financial obligations. This complex relationship sometimes resulted in multiple layers, multiple vassals/lords, and courts trying to sort out who should do what.

On the other hand there were clear differences. The samurai lords started out as local mercenaries operating in conjunction to the military of the court, and then became the military of the court. While French lords started out as Carolingian administrators who gained local power and independence with the fracturing of the Carolingian Empire, the samurai during their initial rise, even in replacing the court's military, worked very much to strengthen the court's control of periphery areas. Even with the rise of samurai and local manors, samurai very much owed their status and control to patrons at court. They were not independent or autonomous of the court in any way. This did not change until the Kamakura, when the Shogunate began down the path of separating warriors from the court. However, specific rituals, rites, and (pre-Tokugawa) ranks were under control of the court in Kyōto, instead of the Shogunate. The court also retained not inconsiderable administrative control during the Kamakura period (something that should not be the case in Feudalism) that was only very gradually lost. Even the power to confirm/reward land rights, the Shogunate actually had not as much as you think, and local leaders had, legally, none. Most of what the Shogunate could offer, at least initially, was military and law-enforcement powers and accompanying titles. Administrative rights and independence from the court (and ironically also from the Shogunate) was won over by local warriors slowly through the (relatively) peaceful 13th century, not during the disintegration of order of the mid-late 12th. Even in the military especially in western Japan, until the Mongol Invasions, the court retained considerable direct control. The strength of the Tokugawa Shogunate and it's rule by domain also shattered the reciprocal relationship (your land rights is still hereditary, but if you pissed off your lord than consider it forfeit, but this also depended on the period), and it had strict law codes and a powerful bureaucracy, leading to questions of whether or not it was feudal. All this, and more, led to tough questions on when feudalism in Japan began and ended.

And so, in the end, the current trend in Japanese scholarship, like that in European scholarship, is to forgo the term all together. If we use it to say mean "decentralized monarchy", it is too broad to help explain the actual situation in any level of detail. If we use a narrow definition ala High Medieval France, we must conclude, due to many differences (I listed some above), that it was not. For sure, like everywhere else, different periods had different similarities and differences with High Medieval France. But if Feudalism means High Medieval France in its purity, then we might as well just use High Medieval France and forget the term feudalism altogether. So now days scholars prefer to just describe the situation as-is, instead of labeling it feudal/Feudal.

Also for /u/ChedCapone

I'm not so familiar with the rules of this subreddit, but in this case I have two cents to add in that someone can improve upon hopefully.

It seems that the rise of both Japanese and Western European feudalism coincided with the decentralisation of power in the region.

In Europe the expansion and divisions of the Carolingian Empire (It was custom at the time amongst Frankish rulers to divide your lands amongst your sons upon your death) meant that a single centralised army was unable to protect the state, and as such the job went to a more localised source. These protectors were given wealth in return, which was in the form of land. This was to be the beginning of the knight class.

Similar thing happened in Japan, during the Heian period the emperor was unable to protect localities and a warrior class emerged to satisfy the need for local protection.