This line of reasoning is wrong, because it is about snap shots and not about trends.
To understand trends you should look at massive data and apply statistics and the mother of it probability. C. Thomson claims Statistics should become a core part of general education and summarizes if you can't write you can't think. The same is now true in math. Statistics is the new grammar.
I estimate the value of data driven methods high, but it has its limits and traps. One is generalization. Predictions out side the working space of your samples might become tea-leaf-reading.
If you are lucky and have a theory you have not only correlations but also causation, and if your theory can be described in the Language of Mathematics you are able to solve its models computationally.
BUT, you quite often cannot describe real world phenomena in their whole scope and complexity by mathematical models . Then do not choose either, but combine data and model driven approaches and let a system that speaks the language of data and the language of mathematics do the computational work for you. Mathematica. Your work is to describe the problem and interpret the results.