Comment 8 for bug 1596027

You shouldn't compare the PPAPI plugin and the NPAPI plugin. They are not exactly the same. This was obvious in the past when the NPAPI plugin was frozen at version 11.2, but it is still true now even though both plugins are version 24.0 (since Dec 13).

In particular, the new 24.0 NPAPI plugin is a security initiative that does not include certain features implemented in the PPAPI version, most notably GPU acceleration of 3D graphics and support of videos with DRM [1]. This new 24.0 NPAPI plugin is shipped by the adobe-flashplugin package, version 20161213, that you are using. Perhaps GPU acceleration of H.264 videos is not supported either? Although that is surprising, that fits your experience of hardware acceleration stopping working recently.

In any case, it's the PPAPI plugin in Chromium and the PPAPI plugin in Firefox (through the PPAPI-to-NPAPI wrapper, browser-plugin-freshplayer-pepperflash) that you should compare. If you do, please consider installing the wrapper from ppa:nilarimogard/webupd8 [2] or ppa:jonathonf/pepperflashplugin-nonfree [3] instead of the one available in Xenial's official archive [4], as this version is already old and hasn't benefited yet of several bug fixes (e.g. bug 1633678).

Also make sure that hardware accelerated decoding is enabled by the wrapper [5]: switch enable_hwdec to 1 in the wrapper's configuration file, and check that enable_vaapi and enable_vdpau are also set to 1 so that hardware accelerated decoding uses VA-API/VDPAU.

[1] http://blogs.adobe.com/flashplayer/2016/08/beta-news-flash-player-npapi-for-linux.html
[2] https://launchpad.net/~nilarimogard/+archive/ubuntu/webupd8
[3] https://launchpad.net/~jonathonf/+archive/ubuntu/pepperflashplugin-nonfree
[4] http://packages.ubuntu.com/browser-plugin-freshplayer-pepperflash
[5] https://github.com/i-rinat/freshplayerplugin/blob/master/data/freshwrapper.conf.example

Have you had any luck with the links I posted in comment 6?