Which client extension support muc/mucLight protocol ?
MUC is supported by almost every client library, MUC Light is supported by Smack and XMPPFramework. Also, MUC Light may be configured to use MUC protocol (with some MUC Light-exclusive features unavailable).
Is there a way to have a shared history for a group using muc/mucLight protocol ?
In MongooseIM both MUC and MUC Light use the same extension and table for archiving so theoretically their archives should be compatible but it is not a requirement so is not tested automatically in the project.
Which is improved for mobile devices ?
MUC Light exchanges data much less frequently than MUC and the packets attempt to carry information as efficiently as possible to reduce round-trips and unnecessary traffic.
any others pros and cons ?
http://mongooseim.readthedocs.io/en/latest/open-extensions/muc_light/#2-requirements
Here are the high-level principles behind MUC Light, that more or less directly indicate differences.