I too have done both, I have an old Simpson and a wooden handled boar brush that I have had and used for well over 30 years. I never hung them until about 10 years ago. Now I hang all my brushes to dry then on the base to store. I have a rotation of about a dozen and collection of about 50 more.

You can buy the plastic stands under 5 dollars. I do dry my brushes well on a micro fiber towel, a terry cloth towel works almost as well, by dabbing the brush tip down on the towel driving the water from the brush into the towel. Then draping the towel over the fingers of an open hand and flagging the brush tips across the edge of the top fingers. 10-20 back and forth laps will leave the brush almost completely dry to the touch.

I do believe hanging keeps the water from the glue plug and may prolong the life of a brush, it couldn’t hurt. On the other hand, I do collect brushes and still fine many old brushes with a full head of hair.