Okay, perhaps this distinction is falling into disuse (the people who like to be pretentious are winning), but if you make this distinction in your writing, your writing will be tighter, less pretentious, and easier to read.
Prior—ahead in order of importance. Think of the phrase, “takes priority,” which still conveys this meaning. ” I’d agree with you, but that would contradict the court’s prior ruling.”
Previous—ahead in order of time. (This word’s teammate is “before.”) “Your previous statement led me to believe you were kidding.”
If you use “previous” or “before” to refer to something that happened beforehand, instead of “prior,” no one will notice that you used the simpler word, but your writing (and speaking) will flow more smoothly and it’ll have a bit more punch.