>>12593975There's a whole variety of problems that are mathematically proven to be reliably solved by linear programs. Linear programs are guaranteed to find the optimum once you prove that you've modelled your problem with the right polyhedron/polytope. Neural networks are more of a heuristic than anything else compared to that.
That being said, I personally don't think either is better, they're different approaches and solutions to different problems and use cases.
You can even solve linear regression using an LP :)