These two combat systems, from the times and cultures you posted, had many similarities between one another.

One difference is that for most Japanese armies (with the exception of the Takeda Clan, and perhaps some others), the elite core of the army revolved around Samurai on foot, while in Europe, the elite core consisted of Knights on horseback. Of course, this does not apply to all European armies or all Japanese armies; as I mentioned, the Takeda Clan fielded so many cavalry that it was referred to as the mounted army, and many of its victories can be attributed to its cavalry.

One similarity is the use of massed formations, consisting largely of spearmen/pikemen. By the time of the Warring States period, formation fighting had become the norm rather than the exception, while in earlier periods combat had (mostly) been forms of single combat. Spears would be the most common weapons among both Japanese and European infantry.

Another similarity is the use of massed archery on foot. In earlier times in Japan, horse archery was the most common form of combat among Samurai, with foot combat mainly being relegated to ashigaru. However, by 1530, most (mounted) Samurai had begun to switch their bows for spears/lances, with most foot Samurai also adopting the spear. The bow was mostly handed off to the Ashigaru in this time, in an ironic switch. Note though that this is a generality. You could still find samurai using bows and performing archery in warfare. In Europe, archers were mostly made up of by peasant classes, so this commonality can be drawn between the two cultures.

One difference, though, is how troops were deployed. By the Late Medieval era, troops were generally deployed seperately according to their type- archers, infantry, and cavalry all were deployed separately but worked together for a common goal. In Japan, for the most part, infantry, archers and cavalry were deployed together and expected to work together. Cavalry would not be deployed in large independent squadrons like in Europe. Also note another difference in cavalry. In medieval Japan, horses were mostly descended from Mongolian breeds and were rather small yet hardy. However, a smaller breed of horse (Actually, most horses in Japan were so small they were considered ponies) cannot perform a direct charge as well as a larger horse. In Europe, larger breeds of horses were available to have cavalry engage in direct charges. Japanese cavalry was more suited to a role of light cavalry- charging flanks and skirmishing. Japanese cavalry did sometimes engage in direct charges (Notably the Takeda Clan, who had access to huge numbers of larger Japanese horses).

As for fighting, there would be a lot of similarity here as well. However, in pre-firearm Europe shields would still be in use by many footsoldiers and those who didn't have access to plate armor. Japanese soldiers didn't use shields, aside from pavises for archers, which are a type of standing shield (Also used by European archers and crossbowmen). Japanese and European swordfighting have a lot of similarities, as well as spearfighting or techniques to fight a fully armored opponent. I don't know enough about this combat to give any specific examples, but I do know that the two cultures shared a good bit of techniques for using weapons.

You are correct that the Japanese (before the introduction of the firearm) did not have access to plate armor. (Riveted iron plate armor did appear very early in Japan around the 4th century, but fell out of use in favor of lamellar type armors). Instead, Japanese armor was mainly small iron scales laced together using silk or leather thread. While not as protective as plate armor, this armor still was designed to protect almost all of the wearer's body from spears, arrows and other weapons. It was protective enough that special techniques had to be designed to combat a fully armored warrior.

One area where lamellar falls behind, though, is with firearms. Firearms have enough force to burst past a laced iron scale, but plate armor has a far better chance of stopping the bullet. After firearms arrived in Japan, plate armor also became increasingly common (Not the same as European full plate, and most commonly a plate cuirass and helmet with more traditional extremity armor, however plate type leg guards and forearm guards were sometimes used), and by the end of the Warring States period was the norm for Samurai warriors. These armors were either imported from Europe, copied from European designs, or developed independently. Less protective, cheap munition plate armors were used by some for Ashigaru as well. =