This is something I've actually given a fair amount of thought to and have been rewriting that chapter on the Governor General earlier this year.
I would say yes: there is very important discretion left to the Governor General to decide whether to do this or to do that. But the most important caveat I now add to that statement is that while the Governor General or Lieutenant Governor has the freedom to make a decision one way or the other in certain circumstances, this is not in fact entirely their personal decision.
Whatever action the Governor General takes must be something that the government at least acquiesces to, so the prerogative powers do not simply say the Governor General can do whatever she wants. It's that the Governor General can do whatever she wants and have a government agree to, whether it's the current government or a new government.
If the Governor General is going to refuse the advice of the Prime Minister, this could lead to a resignation. So the Governor General must know in advance of considering a refusal whether in fact she could form a viable government that would take political responsibility for it. This is something I stress: whatever action the Governor General takes has to be something that the elected politicians are willing to take political responsibility for, whether it's the government of the day or a new government.
So there is discretion, but it's not by any means that a Governor General can simply do whatever she feels is best. She can only do what the current government or a replacement government is willing to acquiesce to and, ultimately, defend to the public.