Doing such a conversion (or supporting both in the same file) was a goal of GeoPackage. It isn't just a schema change though, because of different Y order conventions - you need to use a view to support both; or update all of the tile row indexes.
You can try https://launchpad.net/gpkgtools (disclaimer: I'm the author) for the mbtiles to geopackage conversion - that copies every tile from the source to the destination, but doesn't change the actual tiles.
It is less easy to go the other way (i.e. from geopackage to mbtiles), because there are just so many options in geopackage (not least, potentially multiple tile sets; and various spatial reference systems). Note that getting gpkgtools set up is moderately hard - please check the instructions.
A more general (and way more production ready) option would be to use GDAL. You will need a recent version (like GDAL 2.x) to get the fairly recent improvements. It will probably do a lot more work, and you'd probably need to add the overviews in after the