When would one be used? I don't understand the difference between them.
事【じ】 is a matter, so 大事【だいじ】means a "serious matter".
大【たい】した places less emphasis on the "matter" and more on being "big", so can simply mean "very" or "much".
As an example
As per their negative counterparts, I find that in a colloquial sentence the following would seem a bit more formal:
whereas this sounds more natural: