Neoclassicals and Austrians have different conceptions of “economic laws.” Neoclassicals think that economic laws are empirical-hypothetical propositions like those in the natural sciences. Austrians think that economic laws are logical conclusions deduced from a priori concepts about human action.
For Austrians, economic laws are more like theorems of geometry than laws of motion. The proposition that “in a voluntary exchange each trader benefits” follows logically from the meaning of the terms and the concepts of human action understood by humans a priori. It would be pointless, at best, to treat this proposition as an hypothesis to be tested by gathering empirical evidence about voluntary exchanges. But, economic laws are not strictly speaking “independent of experience” as you put it. They are the framework of meaning for experience. .
For neoclassicals, economic laws are more like the inverse square law. If we abstractly model the force of gravity as being a constant multiplied by the product of the masses of the objects divided by the square of the distance between them, then it follows by mathematical proof, that the acceleration of objects of different mass that are attracted to the same third object will have identical acceleration. This law can then be indirectly tested by dropping objects of different mass and seeing whether or not they hit the ground at the same time. It would be pointless, at best, to treat this proposition as a conclusion deduced from from a priori knowledge.
Austrians further argue that there are no empirical-hypothetical laws of human action. The reason, as Mises put it, is that there are no constants in quantitative relationships of the data of human action. Neoclassicals claim that conclusions drawn from a priori concepts are mere tautologies that tell us nothing more about human action than what we already knew before. Austrians argue that to bridge the gap between our abstract knowledge of human action (i.e., economic theory) and our experience we need another body of knowledge called economic history. Economic history is a blending of the universal knowledge about human action attained by logic and particular knowledge about an event attained by experience. The blending employs judgments of the relevance of the causal factors that bring about a particular event.
The difference between Austrians and neoclassicals is not really qualitative v. quantitative. Both claim to make quantitative predictions, neoclassicals by using their models and Austrians by the method of economic history. And both develop only qualitative economic laws. Neoclassicals do not think that by empirically testing the demand for gasoline over time that the exact same magnitude for the estimates of the parameters in the mathematical equation would emerge. There will be a different quantitative magnitude for the parameter estimates with each data set. In this sense, what they do is not like what natural scientists do in testing the inverse square law. Economists testing the law of demand are just seeing whether or not the parameter estimate on the price variable is negative in each data set.