It doesn't matter... provided that you flick as much excess water as you can out of the brush and then "lather" on a dry towel until the knot is mostly dry to the touch.
Drying your brush completely is the main issue here...not how you dry it. If you have a couple of brushes thus allowing each to dry completely before you use it again then the brushes will have a long life-span. So in short, in my humble opinion, standing it on it's handle is perfectly suitable....