Vinyl's a bit more durable, may be applicable to other materials, and may, or may not, have a harder/softer feel depending on what vinyl you use. Since vinyl is contour cut, you do not have any issues with "boxes" especially on opaque materials for dark colors, there are some transfer papers that can be cut with a vinyl cutter, but they are not intended to be used that way (there was a big
JPSS debate thread a year or so back about cutting it with a vinyl cutter). You can also get special effect heat transfer vinyl films, glitter films for t-shirts, metallics, puff, etc.
Downsides of heat transfer vinyl: Unless you have a solvent printer, you're limited to layering colors in the design. There's extra effort involved in the "weeding" process, removing the vinyl that you don't want to transfer. Oftentimes you may forget to cut mirror'ed, especially if you're doing multiple different things with your cutter.