ISO 8601 and RFC 3339 seem to be two formats that are common the web. Should I use one over the other? Is one just an extension? Do I really need to care that bad?
Is one just an extension?
Pretty much, yes - RFC 3339 is listed as a profile of ISO 8601. The RFC also has some small, subtle differences. For example truncated representations of years with only two digits are not allowed -- RFC 3339 requires 4-digit years, and the RFC only allows a period character to be used as the decimal point for fractional seconds. The RFC also allows the "T" to be replaced by a space (or other character), while the standard only allows it to be omitted (and only when there is agreement between all parties using the representation).
I wouldn't worry too much about the differences between the two, but on the off-chance your use case runs in to them, it'd be worth your while taking a glance at: