What was a basic difference in the beliefs of the federalists and the democratic-republicans

The main difference between these two parties was just who would have more power, the national or the state governments.

The Federalists as the name itself implies were those who supported the stronger federal government as they believed that if the states had more power the country would be weaker and would not be able to address the issue that would impact the whole nation quickly and efficiently. 

The Democratic-Republicans on the other hand, again as their name implies, were more in favor of stronger state governments as they believed and feared that a strong federal government could lead to the loss of freedom they so desperately fought for.