Okay, just to make this clear:
PowerPress for desktop web browsers offers 6 audio and 3 video player options. 5 of the 6 audio players are flash based, the 6th is native HTML5 with Flash fallback. The video players, 1 is flash based only, one is native HTML5 with flash fallback, and the 3rd is VideoJS, a JavaScript library that interfaces between either HTML5 or Flash to provide a styled video player consistent across all browsers.
PowerPress for mobile (Android, iOS, Nokia, Blackberry, Kindle Fire, WebOS etc...) by default uses the native HTML5 player specific to that device. Flash is not an option for mobile devices. The HTML5 player for mobile devices fallback to a play image with a link to the media, so in the worst case when the media is touched to play on a phone that does not have HTML5, the audio/video is immediately opened by the default player on that phone. In most all cases, the solution is seamless.
I would not use a javascript based styled player for mobile devices. As you do your own testing, you'll find what we found, the performance of the player is inconsistent across all the devices, where-as going native HTML5 for the device, the player functions as intended and flawlessly.
The PowerPress solution for mobile playback is the best solution in my opinion, but I do understand the desire to have the exact same player look and function everywhere. But that functionality comes at a cost in performance. Mobile devices just don't have the memory or processing speeds to deal with that added layer, at least not yet.