Thanks, Millie. Sorry if I pontificated a bit.
I also would like to add that the similarities between what you have noted may be due more to how humans naturally act than the fact that we are comparing two religions.
Organizations and especially governments of various types can often have the same type of signature: a hierarchy that seems to control all, a belief system that must be embraced lest you get cast out and even divided from your family, even a "we-have-the-truth" vs. the world philosophy.
For instance, North Korea has these same earmarks. Imperialist Japan up through WWII had them. The Third Reich and even the Soviet Communist system and countless other secular regimes have been like this.
What you are seeing is not similarities of religion in and of itself, but the abusive exercise of power by human beings. Religion and secular philosophies are like guns. They kill no one on their own unless a human operates them.
The Roman Catholic Church did not begin as an oppressive system. On the contrary, it was the oppressed and persecuted and outcast. When the tables turned, it found itself with more than merely the freedom to worship. It found itself with power. When humans get power, the bad seem to find their way to the top in order to grab the reigns.
When the Enlightenment occurred, nations became more secular. The Church lost its power. With only its freedom, the Catholic Church is now similar to what it originally was or at least in a place where it can be what it was once intended. Just becuase Pope Francis is at the wheel steering, it doesn't immediately wipe away those bad humans who rose to the top. These types all like to call "shotgun" and make it hard for a good driver to steer straight. Until they die or you kick them off, the car never travels well, and sometimes the bad passengers attempt to kick out the good driver.
As the other examples I previously mentioned demonstrate, it doesn't have to be a religion to be this way. It can be a secular business that is crooked, even a regime that claims to bring freedom to the masses by liberating the people from religion, only to make themselves the ruling deities.
What you may be seeing in common is what evil looks like, not necessarily a similarity in religions.