Subsampling vs feature selection?

Since we often assume [the manifold hypothesis](https://en.wikipedia.org/wiki/Manifold_hypothesis) or low-intrinsic dimensionality in most cases, I think it is better to reduce the dataset size by feature selection, i.e. the reduction over the column size, rather than subsampling, i.e. the reduction over the row size.

What do @ravinkohli think?