With a fairly clean configuration...
Ctrl+F - opens minifind.
Ctrl+F again, gets to big-find.
In big find
Enter a search string.
Select match case and RegEx
Set color to NotComment.
FIND.
Ctrl+f Ctrl+f to get back to BigFind.
Note MatchCase and RegEx are unchecked.
Bug1: In Tools > Options > Editing > Search, I "Initialize with default options" is OFF - so it should be remembering the options.
If I change DefaultUI to ToolWindow, then the toolwindow remembers its options.
Bug2: "Initialize with default options": This setting seems to have no effect on mini-find.
I'm not sure that it makes sense to either, but then there is conflict about how to initialize big-find when mini-find is enabled.
Bug3: Mini-find is missing "Use default options" command.
Bug4: Set Default Options: Doesn't affect mini-find, and doesn't work in big find when mini-find is enabled (when "Initialize with default options" is on).