Experts and BHG readers answer.
While a 6’6” clearance is low, it should be workable for a playroom. (I am assuming of course you are talking about a playroom for your kids, not your 6’8 husband.) I almost always suggest hanging a drywall ceiling if you can; it just seems to make the room feel more finished. However, you may need to look into some of the flexible fiberglass ceiling tile. These can often be installed tight up against ceiling obstructions. Remember, the entire ceiling need not be dropped lower to hide ducts, you can usually build around them.
One other idea to consider is to simply paint the entire ceiling, beams, ducts, pipes, wires everything. I would suggest spraying this . You will see this in commercial spaces sometimes. It’s a more industrial look but probably OK with a playroom.