I always mix up those two. And if I search for the difference I get confronted with at least two more words that also mean some kind of “important”.
Any help to get those sorted? English is not my first language so the confusion might stem from my German background.
if the sentence has 'not" in it, it’s probably 大した (in most cases),
and if it’s about something you value or care about, it’s 大切.
Thanks. That not part feels like a hack to ace questions on a test. Is there more to it?
大切 means that something is of value to someone on a personal level. it’s “important” in the sense of someone caring for it.
大した means that something is generally impressive or remarkable. it’s “important” in the sense of general significance.
tip: always learn at least three different translations for a word if available, especially if the word has no direct equivalent in English (or German).
if you learn “important, precious, cherished” for 大切 and “great, important, significant” for 大した, then that should give you a better grasp of the meaning of each expression.
it also helps to associate the words with short phrases or word combinations:
大切な友達 - a precious friend.
大したことじゃない - it’s no big deal.
The three translations tip is a nice one 
Additionally, if you don’t mind the effort, looking these expressions up in japanese dictionaries can help get a sense for very specific nuances english translations won’t caputre