I've always been a fan of samurai warfare and history. Recently I've become fascinated with the history and warfare of the Mongolian Empire. Both seem to have emphasized mounted archers on the battlefield. I'm not asking who would win a fight. I'm interested in knowing how similar and different they were, and any other interesting analysis people can provide.
A huge difference would be in the mounts themselves: the Mongols were exceptional horsemen, and had their ponies trained to an extraordinary degree. Plus these animals were naturally agile and very tough. This would give them an edge, along with the sheer number of mounts they possessed (they could switch to a fresh horse and didn't rely on baggage trains).
Unfortunately, I don't know much about Japanese mounted warfare. However, as far as I know, the Mongolians and Japanese only clashed in the Mongols disastrous seaborne invasions (storms and Japanese defenses did not bode well for them).
Here's my sources and some further reading: Bold, Bat-Ochir. “The Quantity of Livestock Owned by the Mongols in the 13th Century.” Journal of the Royal Asiatic Society (Third Series) 8, no. 1 (July 1998): 237-246.
Fragner, Bert G., Ralph Kauz, Roderich Ptak, and Angela Schottenhammer, eds. Pferde in Asien Geschichte, Handel und Kultur/Horses in Asia: History, Trade and Culture. Wien: Osterreichische Akademie der Wissenschaften, 2009. Lane, George. Daily Life in the Mongol Empire. Westport, Connecticut: Greenwood Press, 2006.
Lindner, Rudi Paul. “Nomadism, Horses and Huns.” Past & Present 92 (August 1981): 3-19.
Martin, Desmond H. “The Mongol Army.” The Journal of the Royal Asiatic Society of Great Britain and Ireland, no. 1 (April 1943): 46-85.