See, First You must describe "What is $G$?"
If $G$ is any Type-0 Grammar, then Both Problems i.e. Deciding whether $L(G)$ is CFL or Regular are Undecidable.
If $G$ is any Type-1 Grammar, then also Both Problems i.e. Deciding whether $L(G)$ is CFL or Regular are Undecidable.
If $G$ is any Type-2 Grammar, then Problem First i.e. Deciding whether $L(G)$ is Regular is Undecidable. But Deciding Whether $L(G)$ is CFL is Decidable (Trivial Since Every Type-2 Grammar always generates a CFL But may or may not generate a Regular language)
If $G$ is any Type-3 Grammar, then Both Problems i.e. Deciding whether $L(G)$ is CFL or Regular are Decidable.
So, It Very much depends on the Domain on/in which you're asking the Problems.
Coming to Why Deciding Whether $L(G)$ is Regular or CFL is Undecidable When $G$ is any Type-0 Grammar ?
It's because of Rice's Theorem. Since these are Non-trivial Properties for RE languages.