Birch has the same hardness and durability that comes with a hardwood floor. The only difference is the color variation from light to dark for your preference. Birch generally has light sapwood and dark contrasting heartwood.
When searching for birch wood floors, these are the names (types of wood) of the most common birch:
Paper Birch Paper birch is the softest of the birch wood floor types. It's hardness is about 910 on the Janka scale, a little bit softer than Black Cherry and Red Maple.
Yellow Birch Yellow birch is harder than paper birch at about 1260 on the hardness scale, roughly equivalent to some oaks and green ash.
Sweet Birch Sweet birch is the hardest of the typical birch woods used for flooring. It's Janka hardness rating is 1470 which is harder than sugar maple as well as red and white oak.
