In the new days, rsync -a dir1/ dir2 is the ticket (derived from "is etiquette", if you can believe it).  You need the terminating slash to prevent dir1 from becoming a subdirectory of dir2; dir1/* would of course not copy dotfiles.  (I grew weary of typing "cp -r dir1/.[a-zA-Z]* dir2" to copy dotfiles and dotdirectories left behind.)  The -a flag ensures permissions, symlinks, etc. are preserved.

If you rsync more than once, only the files in dir1 that have changed are copied.  You can also use user@host:path as either argument to make it work over ssh, which is the common use case.