HM. It seems I used to be able to do that. Or something like it. I used to be able to select one pair of characteristics, e.g., size and edge (hard or soft), then retain that choice while adding my choice of Opacity and Flow. And as long as I made one choice first, it would be retained (as the Boss setting) through the second selection. If I picked, say, 25px size with a soft edge, I could then pick, say, 25% opacity at 50% flow, and keep the original size and edge choice, as long as I made the selection in that order. In spite of the fact that both the opacity and flow settings require a dummy "size" setting to be recorded at all. Is that no longer possible? It was once. Opacity and flow can't be recorded in the Brushes pallet, but they can in the Tools pallet, so why not choose a brush, then choose tool characteristics for the brush?
I suspect you may have been referring to Tool Presets (as addressable in the Options Bar).
You may have selected one of those (to set Opacity and Flow) and then a different Brush tip in the Brush Presets Panel previoulsy.
This should still work for Brushes that were saved with »Include Tool Settings« turned off.