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First, like @MatthiasEttinger suggested in the comments, have you had a look at rsync?

First, like @MatthiasEttinger suggested in the comments, have you had a look at rsync?

seems to do exactly what you want. The flags mean:

-a, --archive archive mode; equals -rlptgoD (no -H,-A,-X)
-r, --recursive recurse into directories
-l, --links copy symlinks as symlinks
-p, --perms preserve permissions
-t, --times preserve modification times
-g, --group preserve group
-o, --owner preserve owner (super-user only)
-D same as --devices --specials
 --devices preserve device files (super-user only)
 --specials preserve special files
-A, --acls preserve ACLs (implies -p)
-X, --xattrs preserve extended attributes
-E, --executability preserve executability
-v, --verbose increase verbosity

seems to do exactly what you want. The flags (used or implied here) mean:

-a, --archive archive mode; equals -rlptgoD (no -H,-A,-X)
-r, --recursive recurse into directories
-l, --links copy symlinks as symlinks
-p, --perms preserve permissions
-t, --times preserve modification times
-g, --group preserve group
-o, --owner preserve owner (super-user only)
-D same as --devices --specials
 --devices preserve device files (super-user only)
 --specials preserve special files
-A, --acls preserve ACLs (implies -p)
-X, --xattrs preserve extended attributes
-E, --executability preserve executability
-v, --verbose increase verbosity
 --delete delete extraneous files from dest dirs

$ rsync -aAXv --delete /path/to/source /path/to/backup/folder

seems to do exactly what you want.

$ rsync -aAXEv --delete /path/to/source /path/to/backup/folder

seems to do exactly what you want. The flags mean:

-a, --archive archive mode; equals -rlptgoD (no -H,-A,-X)
-r, --recursive recurse into directories
-l, --links copy symlinks as symlinks
-p, --perms preserve permissions
-t, --times preserve modification times
-g, --group preserve group
-o, --owner preserve owner (super-user only)
-D same as --devices --specials
 --devices preserve device files (super-user only)
 --specials preserve special files
-A, --acls preserve ACLs (implies -p)
-X, --xattrs preserve extended attributes
-E, --executability preserve executability
-v, --verbose increase verbosity