Excluding the church for a moment, I believe that, in their extreme, these government systems all come out to exactly the same thing. And, interestingly, it is the exact opposite to that which God has established for the church.
Man has had systems of government of some type since Adam arrived. Most governments are made up of bits of these systems. For example left wing governments (Communism, Socialism, Democratic Socialism and National Socialism (Nazis)) are about government control or involvement in industry and providing state services. Yet almost every country has a government providing some service for the people. And then there are defense contracts. Right wing governments (Capitalism, Republicanism, Kings and Judges) are about freedom of commerce and not getting involved in industry or government services. Again, almost every country has some degree of economic independance of the people.
Government Systems:- These are run by a Chairman, President or whatever he may be called. He has a small group around him that have control over industries, police, services etc. Under these are the remainder of a fairly larger council or government body of representatives. From there they branch out to local area leaders.
But what happens when these governments go to their extremes? We have seen what happens in history (some fairly modern).
The leader obtains great control by giving lots of power to his small group of aides. To make their power great he has to increase the power of his council. To make their power greater he must increase the power on the local level. Whether right or left wing, people will act exactly the same with power. The powerful people will live in better areas and better buildings, with far more access to provisions. They will have the power to exercise injustice. And this won't bother them in doing so. These powers are obtained because the people are weak through sin. They have little power of conscience. They seek revenge above repentance on those who offend them. And on criminals. Interestingly, a wise man once said that you can tell the strength of a people by how well they treat their prisoners. And these government systems show less and less interest for human life.
Now let's look at how the church should be run according to Scripture. It is an exact opposite of this system. The church has exactly the same as the "Government Systems" paragraph shown above. But the difference is that Christ taught that he came to serve, not to be served. Paul said that he made himself servant to all that he might gain more (1 Cor 9:19). D&C 121:37 tells us that leaders have no authority to use their position to attempt to have power over others. The church should be seen exactly the opposite of how we see governments outside of God's Kingdom. We see governments as a pyramid. The President at the top, his 12 leaders as the next section down and so on. But the church should be understood as an upside down pyramid, with the President down the bottom serving the whole (as any good government should be - as demonstrated by King Benjamin) and the members at the top being served the most. What we term "church leaders" should be called "church servants". This is the thinking Christ demonstrated.