What are the pros and cons of covering a basement ceiling with drywall vs. panel board?
For insulation (either thermal or acoustic) use batt insulation between the joists (e.g. Roxull or other mineral wool type which seem better for sound insulation purposes).

For additional soundproofing and a finished ceiling, you may want to consider a resilient channel ceiling, with some kind of removeable tiles (e.g. http://www.homedepot.ca/product/resilient-channel-x-12/968159).  This could lose you less ceiling height than a drop ceiling.

One consideration for having the ceiling be removeable is that you may want to run wires/pipes for the finished area of the house in future.