Irrational, unreasonable are comparable when meaning not governed or guided by reason.
Both terms have been used occasionally in the sense of not having the power to reason. Except in technical senses (as in mathematics) both words apply usually to men, their acts, utterances, feelings, policies, and demands.
Irrational may imply a lack of usual or normal mental control and powers, but more often it suggests a lack of control or guidance by the reason, or direct conflict with reason's dictates; it therefore comes close to absurd, illogical, foolish, preposterous, senseless, or fantastic.
Unreasonable implies guidance or control by some force (as self-will, passion, ambition, greed, or stubbornness) which makes one deficient in judgment or good sense. As applied to one's acts or utterances, it suggests lack of justification by reason; the term therefore comes close to inequitable, immoderate, excessive, unfair, or extravagant.