Both refer to reasoning. Having said that, there's a slight difference. 理性 indicates a person's characteristics, while 理智 demonstrates a person's intellectual ability to make sound decisions.

理性 and 理智, these two words can be used as noun and adjective to describe someone who's smart. But We use 理性 to describe someone's personality. say 他是个理性的人. It's paired with 他是个感性的人(he is a sensitive man). However 理智, we use it in a more particular situation, e.g. 当Jim被Sam激怒时，他没有失去理智和Sam打架(when Jim was provoked by Sam, he didn't lose his control to fight with him). We say Jim dealt with the situation in a very smart way. In short, use 理性 to describe something abstract like a person's personality and 理智 when people are smart enough to deal with a particular situation.

理性 = innate wisdom 理智 = wisdom gained through study, knowledge, experience etc. Similar to nuances in the meanings of being "streetwise" vs "book smart"

Generally there is no difference between these two words. They are synonyms no matter being used as adjective or noun. Choosing which word depends on your preference and habit.

Hi, glad to help. ‘理性’ describe a characteristic that someone copes with problems with knowledge, experience, other wise persons' advice. It is often used to describe a person's behavior pattern, so this means someone always acts like this. The opposite is '感性'，means that someone solves problems by his intuition. '不理智' means someone had a sudden impulse to do something worthless, or he losed control when he coped with a problem in the past. But this doesn't means he has this personality, it can be only occasional.