palou89's input is something I would agree with. I've never noticed what "we all know and are told," only that whether or not the airplane is co-ordinated, will have the predominant effect on which wing drops. And if you want to get picky... a dented wing, other minor dirt/damage will also play a part. Even different angles of incidence would affect it, as one wing would have a (slightly) higher AoA that the other, so would already be nearer to a stalling AoA. Another difference between climbing/descending is the thrust, and slipstream over the wings, also playing a major role in both scenarios. (I'm assuming climbing stall=power ON, and descending stall=power OFF??)
I think that dihedral also has a part to play in all of this, due to the varying vertical lift components... especially in the climbing/turning scenario. But then, for descending, the low wing would appear to have the advantage of a greater vertical lift component. So you could put this down to the outside wing travelling faster (further to go). Also, washout could be a consideration.
Forces in the turn would be another factor.
All this talk of staircases seems too complicated, especially as there are more factors to take into account than just the relative wind... [I initially assumed the handrails (which are level) represented the path of the wings, and not the airflow (relative wind). It's the first time I've heard of this analogy.]
You could have a look through
Handbooks & Manuals at the Airplane Flying Handbook, and Pilot's Handbook of Aeronautical Knowledge by the FAA. I don't think they go too far into climbing/descending stalls in turns though??