Let me preface by saying that I'm not a great expert on this.
Secondly, I think you'd get a different answer from each state from what you'd get from the federal level.
The principle, of course, is that the total funding does not alter. How it's delivered is an organizational issue, and the funding is supposed to relate to the issue and not to who does it.
I'm just making a guess, but I think the very fact that the states have been contemplating voluntarily giving more authority to the federal level seems to indicate that they see a concern, not so much for the amount of money they're getting now, but with the future commitments they'll have to face as the population gets older and with the sorts of health issues we have in western societies these days.
That said, there has been a lot of disagreement between the federal and state areas about the most efficient way of delivering good health care. In fact, it was an issue in the last election. The previous Conservative government took over two hospitals forcibly from state authorities because they said the state authorities were not doing a good enough job in managing them and using the funds that were available.
As far as I know--and as I say, I'm not an expert--it seems to be more a question of organization of the portfolio than absolute levels of funding.