In American English, judgement is generally considered a misspelling of judgment for all uses of the word, notwithstanding individual preferences. In British popular usage, judgment was traditionally the preferred form, but judgement has gained ground over the last couple of centuries and is now nearly as common as judgment.
Pay no attention to the myth, widely repeated on the web, that judgement is the original spelling and that judgment is a 19th-century American invention. This is simply untrue, as shown by an abundance of readily available evidence anyone can view online.
When it comes to legal contexts, English reference sources say varying things. Most seem to agree that judgment is preferred in legal contexts even in British English, and some say that American and British English differ in their strict legal meanings of judgment. Bryan Garner, in his Modern American Usage, says judgment in American English refers to “the final decisive act of a court in defining the rights of the parties,” whereas, he writes, the word in British English refers to a judicial opinion. We find nothing to contradict this, though there are many English reference sources that do not mention a legal/nonlegal distinction or an American/British distinction.