You can do that with MapInstall as well. This may help:
https://support.garmin.com/support/searchSupport/case.faces?caseId=%7B5af8a260-fd05-11dc-ec92-000000000000%7D
Basecamp includes MapInstall, so your equation isn't quite right :)
It's just that in Basecamp installing maps is launched/handled in a different way to the way it was done Mapsource.
I cannot do this with BaseCamp.
I must have expressed myself in a confusing manner then. We still use the same gdb format that we used in MapSource, just a newer version. MapSource cannot read the newer version, so therefore it's not compatible in that sense (try opening AllData.gdb in MapSource). But BaseCamp still exports the age-old gdb that MapSource understands.
Switching from the binary gdb format to a real database is something we really want to do.
Since this seems to be the biggest BaseCamp vs. Mapsource thread...