Whats the difference in doing the shoulder bar dislocation stretch with a regular wooden rod vs a towel/rope? (Note: I know the second picture is using a towel, but I use a rope and pull it wide tight).
Unfortunately I can't explain the exact mechanics of it, but essentially the difference is with a pole your hands / arms are fixed into a certain rotation (let's call it parallel), whereas with a towel / rope / band your hands and arms can rotate to place the shoulder joint into a more comfortable movement pattern.
I find using something flexible easier as it allows me to externally rotate my shoulders as they pass over my head, allowing me to drop my arms lower behind me.
However, I believe that I get a better effect from a solid object like a broomstick as it forces the shoulders to stretch the particularly tight muscles at the front of my shoulders, rather than allowing shoulder rotation to find an easier way to move.