Other than juicio, which has the additional meaning of a legal trial, these words all have to do with wisdom, judgement, and/or sense, as I understand it.
In what ways are they different?
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Cordura, sensatez and juicio can be (and are) used as synonyms according to RAE, but in everyday speaking (this is my view on the matter):
Cordura: Sanity (opposed to madness)
Sensatez: sense (opposed to imprudent)
Juicio: Kind of old-fashioned, but used in sentences like "Has perdido el juicio?" (Have you lost your mind?)
Sabiduría means Wisdom and can be used as a synonym of the other words but usually is understood as a person with lot of knowledge, academic or any other kind.