What aspects of a republic make it prone to faction, but less susceptible than a democracy? (Federalist No. 10)

The main aspect is that there is local control of the government on some level makes it susceptible: this leads to people choosing up sides when things start to go wrong. However, compared to democracy, which has much more local control, a republic is less likely to run into this type of separation of powers issue. Republics have much less local control than do democracies.