The differences between the two are so broad that it couldnt be told easily. But to share an example, the voting rule are what separate the two and what make a republic government more suitable to America. Basically, voting and decisions are made based on the constitution as well as the people as individuals themselves.
I consider myself to be independent, but based on who is in office and the state of the US I will have to go with Republicans. The country is in need of a change right now and that change would be Republicans. I'm not convinced they will be much better but at least try.