Is it possible to use one video type across all browsers?

Since we are using an HTML5 video player with Flash fallback (meaning Flash is utilized if the browser does not support HTML5), you are able to create a single file which will play on all major browser types, including iOS. Our recommendation is to encode your mp4 videos in H.264.

MediaElementsJS supports most mainstream browsers as well as mobile browsers, however, support for older browsers has been dropped (supports IE11+, Chrome, FF, Safari, Android 4+ and iOS 8+). WordPress will be updating MediaElementsJS to version 4.2.6 and has stated the browsers requirements  here

S3 Media Maestro does not use the MediaElementsJS player included with WordPress. The reason for that is so that we can stay current with the MediaElementsJS player regardless of how often WordPress decides to update it in core code.