8 years to develop the Saturn rockets and all the associated lunar module gear, without any ability to do sophisticated computer modeling or simulatoins. That's pretty competitive; SpaceX is about 20 years old now.
But that's not the point. The point of Falcon 9 was to reduce the price of getting to space. That was purportedly the promise of Ariane 6 but now there has simply been goal post moving to "it's to maintain independent access to space".
What is the EU spending compared to what SpaceX spent to develop its launch vehicles?
Government did much less stuff in 1960s, that was before the Great Society and many other things. 4% total budget in 1960s and 4% in a modern Western state are totally different things.
Is the state sponsorship the same in both cases, or are there noteworthy differences?
By hiring private contractors and throwing lots of money at them.