Fascism and Crony capitalism are essentially the same thing, Holmes
I'm glad we can agree on that Watson
Industry is technically in private hands, but the market is controlled by government.
Not exactly, industry and the government have become the same. Capitalists control the government that controls the markets. No more free market crap, just a happy moneymaking machine run by the oligarchs for the benefit of the oligarchs.
Both of them are forms of socialism.
No, socialism works the other way. In it's most extreme form the government (which is "we, the people" in theory, "we, the communist dictatorship" in practice) controls everything. No more free market anymore but exactly the opposite of fascism.
Capitalism is economic freedom. That government controls free markets is an oxymoron
Economic freedom is an illusion, capitalists always want more $$$ and seek to eliminate the competition. The end result is fascism. Pure socialism is also an illusion, it's simply incompatible with human nature to expect them to share everything. If that ideal is forced on a population by (well meaning?) revolutionaries the end result is communism.
The only thing that will work is a combination of the two