You're quite right that CH is not an example of a Godel sentence which demonstrates incompleteness (examples of that are given in the linked article) -- I didn't mean to imply otherwise. I just wanted to share that this was a more practical example of incompleteness in our modern mathematical framework (ZFC) which folks might find interesting.
But as others have said, both statements are equally unprovable in ZFC. The Godel sentences demonstrating incompleteness are constructed in such a way that you could argue (outside of the axiomatic system) they are provably true or false, while CH is a case where reasonable mathematicians may disagree on whether it is true or false. But ultimately there is no proof in ZFC for either, so they are both examples of incompleteness in ZFC.
And note that the Godel sentence demonstrating incompleteness doesn't need to be true -- the inverse of the Godel sentence demonstrating incompleteness is also unprovable.
But as others have said, both statements are equally unprovable in ZFC. The Godel sentences demonstrating incompleteness are constructed in such a way that you could argue (outside of the axiomatic system) they are provably true or false, while CH is a case where reasonable mathematicians may disagree on whether it is true or false. But ultimately there is no proof in ZFC for either, so they are both examples of incompleteness in ZFC.
And note that the Godel sentence demonstrating incompleteness doesn't need to be true -- the inverse of the Godel sentence demonstrating incompleteness is also unprovable.