I find that having the brim down increases downforce but I tend to keep my head down, just peeping out under and and around the brim (particularly against car headlights at night). In the dry, I have the brim up, though some modern-style caps have a too-stiff pre-shaped peak for that to be comfortable.
I was kind of hoping for something with a rubberised band round the inside or suchlike, to increase friction without excessive tightness. The only rain cap here with one of those bands (Sealskinz) has it sewn on the bottom edge only, so the band tends to turn itself inside out as the cap creeps up my skull before flying off.