When you click to open a subtask on the right board (having all the list of tasks on the left), you get to see the detail of the subtask on the right, but the list on the left doesn’t change. As things are now, when you dig into the detail of a subtask, you loose the detail of its parent task. You only see the name of it, and all the other tasks on the left, including those that are not related to this particular subtask.
It would be useful to allow a view in which you have the detail of the parent task on the left board and the detail of the subtask on the right. Just that.