Just as an addition to the other answers:
There's no need to make this an either-or situation -- you can have an electronic board and a physical one.
Our team uses an electronic board as the main working tool (we use Kanban) and as the authoritative source of information. The electronic board has all tasks, is updated as tasks are worked on etc.
In addition to that there is a physical board, which only has major stories. It is mainly meant to create visibility, especially to outsiders, such as PMs and stakeholders.
This does mean that changes to the electronic board need to be manually replicated on the physical board, but this is doable, as only major stories are tracked there, which usually take at leas a day.
We find this a good combination: The electronic board is useful for small stuff, for day-to-day work and for metrics, and allows comments, links to specs etc. The physical board gives a quick overview of project state and makes it easier to see the "big picture".