One requires unlimited government power and the other requires government to be separated into different parts

One seeks to temper the government's exercise of power and the other reflects a grant of absolute power to the government 

One requires that government power be split and the other dictates the way that government power should be exercised

They are different concepts -- so they cannot conflict with one another

The Rule of Law is just one of the virtues which a legal system may possess and it requires that people should be ruled by the law and obey it and that people should be able to be guided by it.

The Rule of Law is the principle that everyone is subject to the law, regardless of their social status or position and the laws that are made should not be arbitrary, and that constitutional principles are the result of judicial reasons.

The Rule of Law requires that all persons and authorities within the state afford adequate protection of fundamental human rights and requires states to comply with their obligations under international law.

The rule of law is more than regularity or predictability: it imposes a requirement of justification, connecting restrictions on liberty to a public or common good. A law that fails to comply with this function is not a law at all.