Greetings. There are varying opinions on this matter. IMHO it is better to use a stand as it prevents water from gathering in the knot. The force of gravity also helps it to dry the bristles faster, by drawing water away from the handle. Hope that helps.
If you have a animal hair brush made from badger, boar or horse hair then I think it's a good idea. It's is a good idea to remove all the soap from the brush and dry it a bit on a towel & storing it in a well ventilated place. I have a synthetic brush that I store the same way but there really is no need as it's not going to come to any harm.
The only brush I hang in the stand is my badger brush, mainly because it came with the stand. All others, boar and horse hair brushes get stood up on their handles. I honestly don't believe it makes that much of a difference. Dave
If you dry your brush(es) enough that they aren't dripping wet when you put them away, it makes no difference other than personal preference.
Drying(as in damp drying on a towel after your shave) and storing in a well ventilated area are more important than bristle/hair direction.
