Q:

When is the correct situation to use 案外 or 意外?

I think this is a question I should have asked a long time ago.. What is the difference between 案外 and 意外? What does the correct situation look like when using either?
Example with 案外:

人生は案外短いものです。ですから、こんなにも貴重な人生を、自分が満足できない仕事で無駄にしているなんて、驚くべきことです。

Example with 意外:

意外なことに、とてもうまくいってます。

The English translation definitely didn't help me with this one, as both are "unexpectedly". Is there a certain degree that is associated with each?

A:

I've always thought of them in terms of their kanji make-up.

案: can mean "plan/expectation"
意: can mean "idea/mind/thought" (with the thought process maybe implying some subjectivity)

From there:

案外: 

"not according to plans/expectations"
"[contrary to/against] expectations"
often, but not always "disappointing(ly)"

意外（に・と）:

"[against/not] what was [thought/expected]"/"(I/you) wouldn't have thought"
"surprising(ly)"

Daijisen has some usage notes differentiating the two in the definition for 案外. I think it basically says:

案外 is used when expectations/situations turn out different:

期待していたが、案外つまらない映画だった
  I had [expectations/hopes], but it was a disappointingly boring movie.
心配していたが、仕事は案外楽だった
  I was worrying, but contrary to expectations, the job was easy.

意外な/意外に are used when the reality is different to what was thought, or with things that can't be expected:

意外に時間が早くたってしまった
  Time passed surprisingly quickly.

