Yup ... have it from our first floor to the second floor on one of the staircases. First floor is hardwood; second floor is also hardwood. Stairs are carpetted, as they're in no condition not to be covered and doing anything else would be a can of worms. Second floor landing used to have carpet, just up to the doorways to bathroom and bedrooms, but it was possible to remove when the carpet was replaced, as the landing has the same floor as the bedrooms. The transition from wood floor to carpetted stairs doesn't look odd or out of place. I think a transition to carpet on the stairs is simpler and less apt to clash than picking one flooring or the other to refinish in. If you do have to pick one, I'd go for matching the wood of the first floor unless there's a door at the top.