What are the differences in their economic ideology?
What is economic ideology?
Classicals held to a labour theory of value whereas Austrians hold to the marginal utility theory of value. Classicals treat economics as the science that studies the production of wealth, whereas Austrians treat it as part of the science of human action. Have a look at George Reisman's works on the Classical economists for a revised view though.
Freedom of markets is positively correlated with the degree of evolution in any society...
Jon Irenicus:Classicals held to a labour theory of value
An interesting side-effect of this was that some classicals held that increasing nominal prices were good because these prices reflected a high amount of labor expended on a product. They also held that increasing nominal prices would lead to decreasing real prices. But I'm not an expert on classicalism but I did read Wealth of Nations and the above is basically an interesting monetary view that conflicts with austrianism.
But does anyone know if classicals held a theory of the business cycle? I can't find one.