If you are wanting to make a high end boarding barn then everything must be as safe as possible. I would not choose either of those fences for my "best choice" although the wood is better. As far as for the barn? I would hire a reputable builder to make sure that your ventilation, etc.. is up to snuff. So many barns end up with condensation issues and black mold, or dust.
If you want a middle to lower end barn, then put in what is economical and safe. A modular barn would be good for this route too.
Basically, if you're expecting to charge $600/mo and up for indoor board, your facility needs to be very good. Anything lower and you can skimp on some expense. Personally, I don't really care how stuff looks as long as it is safe and clean. Safety and cleanliness tend to go hand in hand.