I don't see a need to over-think this one. An "evidence-based" conclusion would be any conclusion based on objective evidence, whether that evidence were thoroughly researched or from an authoritative source, or not. The term simply indicates that you are basing your conclusion on what you perceive to be a fact. For example, to say, "He tripped because he stepped in a hole" is an evidence-based conclusion where there is no extensive fact-checking or authoritative sources, just a single, simple, obvious fact supporting a single, simple, obvious conclusion.
A "faith-based" conclusion would then be any conclusion that was not based on what you perceive to be a fact, but based solely upon your beliefs or your emotions - your hopes, fears, ideals, etc. For example, if you were to say, "I know that my son will do the right thing in difficult circumstances," that is a faith-based conclusion with no religious connection. In this broad interpretation of "faith" it is synonymous with "belief" or "believe" which does not necessarily imply a religious belief.