I have 2 browsers, Opera as main browser, but only 1 site of all websites left uses Flash. The problem if I would install Flash as plugin for Opera is that many websites now will see the 'User has Flash' flag in Opera browser headers and will serve you a Flash version instead of HTML5.
This is where Firefox comes in with flash-plugin-nonfree, if I need Flash I startup Firefox since installing Flash for Firefox is easy. In Firefox I too notice many websites detect the Flash and many sites refuse serving HTML5 because of the 'User has Flash' flag Firefox gives. Even when flash is 'play on click' only.
Flash does for example no longer offer hardware video decoding on Linux like it did in the past. Flash is usable on for example speedtest websites, or websites with a lot of many small Flash games.
My conclusion, installing Flash as a Pepper plugin or somehow inside Opera or Chromium e.g. will have serious side effects on your daily browsing.
My solution, Firefox for the seldom use, and Opera for daily use. It's strange one cannot make Flash undetectable in Firefox unless one disables or uninstall Flash completely.