Hi,
I’m completely noob to MyPaint so maybe I’m missing something, anyway let’s say I have brush A selected and I change its “Sharp” setting; then I select brush B, and then again brush A; brush A “Sharp” setting won’t be the one I had set before but the default one. It would be better, I think, if every brush remembered its settings… but maybe again I’m missing something 
MyPaint 1.2.1 on Arch Linux, XFCE, Wacom Bamboo One M CTL-671
There are a few options you can do. You could save the setting into the brush by opening the brush editor and clicking save after you modify the sharpness. But only do this if you really want this to be permanent.
Another option is to use the brush/color history panel to select the previous brushes which will include any changes.
Another option is to save the brush as the hotkeys 1-0 which will include any changes you made to the brushes. Use ctrl-# to save the brush to a number.
Another option is to use the pick stroke key to grab the settings of the brush right off the canvas. This option can be trickier.