For some context, I heard during a college class that the Pope was similar to the Japanese Emperor, but always thought that was wrong.
It seemed to me that the Holy Roman Emperor had more in common with the Japanese Emperor, and the individual lords had more in common with the daimyos with with the Kings acting as something similar to the Shogun.
Is this correct?
Also, was the “Old West” similar to either? It seems to me that the time between the Civil War and Great Depression was similar to these systems as the landlords were effectively daimyos with serfs.
The three have very little in common.
The Holy Roman Emperor was elected by the electors. He had substantial land holdings and power, issued laws and edicts, raised armies, and often commanded them in person. However even though the election was often just a formality, the fact that the Emperor's power derived from the electors greatly limited what he could do. The king of Bohemia and other Prince/Dukes of the empire had no formal power outside their own realm.
The function of the Japanese Emperor changed significantly over time, but since you mention daimyos and Shogun I will assume you are talking about a rough time period between the 14th and 19th century. During this time the Japanese Emperor had very little land and income and did not pass laws. He did appoint the Shogun, but that for the most part was a formality. Any edicts he issued that did not concern the regular functions of the court (religious and court rituals, appointments, etc) for the most part was issued on the wishes of the Shogun, and the Shogun's government bore a lot of the cost of regular court functions. The Shogun had significant powers over the daimyo that many Holy Roman Emperors would likely die for (some might have) since the position was not elected. How much say individual daimyos had in the Shogun's government depended on his clan and ranged from being the vital ministers to absolutely none at all.
Finally, I do not believe the land lords of the old west past their own laws (not informal orders, actual laws on the books backed by the lord's theoretical monopoly on violence), built huge fortresses and associated towns, and mobilized hundreds, thousands, or even tens of thousands of soldiers to fight their neighbours, and engaged in diplomacy and marriage alliances. I also don't believe those land lords developed a set system of bureaucracy of either letting on-site collectors tax-farm, straight-up giving followers land income rights in return for mobilization in times of need, straight up direct bureaucracy, or some combination of all three. So unless I am greatly mistaken in my American history then no, the system of landlords had very little in common daimyos and serfs.