The whole Falcon program, including new engines, Falcon Heavy, reusability, human rating, multible launch sites all in all cost considerably less then 4 billion $.
The Ariane 6 alone cost 5 billion and likely the total cost until it launched is gone be quite a bit more.
But what people dont understand is that lots of parts of the Ariane 6 arent in its own budget. The upper stage engine has been in development for 20 years. The solid booster tech is its own thing. The core engine is a minimal evolution over the earlier version.
A lot of institutions involved in the development have their own seperate government funding.
If it takes you 5$ billion to do a minimal evolutionary update of the Ariane 5 (with parts already developed for the Ariane 5 ME). Then what would it have cost to develop a totally new reusable booster? 10 billion? 20 billion?
Europe also talks about crew vehicles, but that gone also cost them 7-12 billion the way they develop, and thus it will never happen.