I assumed you would be painting in a coordinating dark color. There exists special high-traffic floor paint, but it's not worth the expense for just a couple of thresholds unless you can get a small tester size and can live with the slightly different hue from the door paint.
Staining will hold up better, but shoes will eventually wear the stain lighter in the traffic spots. If I were you, I'd paint everything the same color as proposed and then simply give the painted surface a couple coats of polyurethane (flat, matte or satin) after the paint has had a good solid week or so to dry. Sand the painted surface with 400 grit prior to poly to give it a "key" and allow the poly to hold better. You probably already know this stuff, but covering it just in case you didn't.