Virtual Directories are handled in a more consistent manner (in particular between Azure Storage and S3).
If you have virtual directories (ie blobs with / in the name indicating directories... eg mydir/myfile) then you can perform the following
azurecopy -i http://...../mycontainer/mydir/ -o https://........
This will copy all blobs with the prefix "mydir" and copy them to the destination but will trim the "mydir/" prefix from the destination blob. ie it pretends to copy the inner file and keep the inner file name.
If you want to copy everything in a container/bucket and keep the virtual directory structure you can perform the command
azurecopy -i https://..../mycontainer/ -o https://......
This will copy all the contents of mycontainer to the destination, keeping the exact filenames (including virtual directory delimiter /)