Pick a metric. Fourier is probably better in general.

With respect to machine learning, probably the fact that Fourier is bounded and gives coherent (if completely random) results even very far from the interval of interest.

However, this is like saying that an O(n log n) algorithm is better than O(n^2). Sure, it's true in the limit, by the constant terms can be quite large and O(n^2) can remain better up to remarkably useful values of n.

As I pointed out, the advantage that polynomial basis generally has is that you can be accurate enough with lower powers that are much, much faster to calculate (we use matrices of linear equations precisely for that reason). Or, you can match a particular process because you know specifically that it follows some particular function (we know that road damage follows the fourth power of load--it would be counterproductive to model that with Fourier).

Using high powers for polynomial basis is almost always worse than any other choice.