Hardwood is actually a botanical classification for a deciduous tree, one that loses its leaves every year. Hardwoods generally are harder than softwoods (coniferous trees). Does that make any difference in the choice of species for the mouldings you choose? It can, depending on the usage. For example; Red Alder is a medium soft wood that would not stand up very well as a stair tread. Cherry is harder than alder, but as a flooring material or stair tread, it will dent and show wear much more than a harder wood like red oak or hard maple. Poplar is a great wood for painting. It is 15% harder than white pine so will stand up to more abuse without denting. Continuing the same thought though, if one wanted a better, more dent resistant wood, hard maple or birch would be a good choice. Here is a listing of hardwoods and their relative hardness. Hickory is the hardest species listed and is assigned a hardness of 1. The rest are a comparison to this standard.
Hickory - 1.0, White Oak - .94, Hard Maple - .88, Red Oak - .88, Yellow Birch - .86, Black Walnut - .80, Soft Maple - .78, Cherry - .73, Yellow Poplar - .63, Red Alder - .58, Aspen - .55, White Pine - .55, Basswood - .50.