Subtypes are typically used to ensure data validity.
Representations, on the other hand, are specifically employed in displaying data. Representations allow more display options than the standard symbology, and in particular are helpful in that they allow one to display data in different ways without altering the source data. For example, if one had two coincident lines in GIS to display, like bus routes on the same road, with Representations one could show them side-by-side for reader clarity instead of overlapping each other. And the original data would not need to be altered to do this.
Chris Donohue, GISP