Mobile GDB:
One of the benefits I've found when using mobile geodatabases is that they're easy to share since they're just a single file. For example, I can easily attach a mobile geodatabase to an Esri support email -- without the file being blocked (i.e. a multi-file FGDB as a zip) or needing to deal with FTP.
File GDB:
Of course, a benefit to file geodatabases is that they're fast for spatial operations.
What are some other benefits/considerations when choosing mobile vs file gdbs for new projects/tasks? For example, mobile geodatabases have full SQL support, whereas file geodatabases do not.