Regular Language - Context Free Language
Your second method to arrive at $\phi$ is bogus - consider the case where $B$ is the empty language. Where you are confused here is you are looking at the difference between the sets of all regular languages and all context free languages, instead of the difference between the two concrete languages.

The correct answer is d. None  (you can't say anything)

Because 

$R=\overline{A}-B = \overline{A \bigcup B} $

Since $A \bigcup B$ is clearly a $CFL$, this answer applies which states that the complement of a $CFL$ is not necessarily $CFL$ itself ($CFL$ are not closed under complement).