Mozy is similar to Carbonite. The advantage of backing up to a local drive is the ability to deal with a complete hard disk failure without having to redownload hundreds of gigs of data. Mozy, Backblaze, and Carbonite are great for a second line of defense, say one loses their computer and their backup drive. However, it is nice to just restore a file with a click, than to have to find decent Internet access (or burn up precious gigs on a LTE connection) to restore.
Not saying Carbonite is bad. It has its place. However, the first line of defense is an external HDD, if possible.