Media gallery is currently incompatible with the 2.x branch of Media. The changes needed to make it compatible look to be relatively small.
The current consensus seems to be to make these changes in a 2.x branch of media_gallery. There is a current patch. However, despite efforts to limit the patch in #1391332: Support file field as well as deprecated media asset field to introducing file field support in mediafield 1.x (see the issue summary), that wasn't done and instead the commit in that issue introduced some fairly messy code aimed at supporting both media 1.x and 2.x in the same branch, see http://drupalcode.org/project/media_gallery.git/commitdiff/0e94214. So work will need to include a partial rollback of #1391332.
- Remove the workarounds that were introduced in #1391332: Support file field as well as deprecated media asset field to support both media 1.x and 2.x in a single branch of media_gallery, leaving just media 1.x support.
- Create a 2.x media_gallery branch.
- Adapt the media 2.x changes that were added in #1391332 and add them to the current patch.
- Ensure the patch still supports existing 'media' fields (since they are deprecated but still supported in media 2.x/file_entity 2.x).
User interface changes
Original report by dddave
The new branch of Media module seems to be the place where the magic happens in the future. Currently this module depends on the 7.1x branch. I don't know if this would mean creating a new branch for media_gallery or if it could work with Media 7.2x with a few tweaks.