Refers to a formal or authoritative judgment, often in legal, moral, or evaluative contexts. Can also imply a decisive ruling or assessment.
裁判官は公正な裁きを下した。
The judge handed down a fair verdict.
The judge handed down a harsh verdict on the defendant.
His judgments are always strict.
He ended up being judged by the law.
The culprit was going to be brought to trial.
審判 emphasizes the act of deciding or arbitrating (as by a judge, referee, or deity), while 裁き focuses on the resulting verdict itself.
裁き (judgment, verdict) and 捌き (handling, managing, e.g. 手捌き) are pronounced identically but written and mean completely differently.
The noun form of the verb 裁く (さばく, 'to judge'), derived from the kanji 裁 meaning 'judge' or 'decide'.