The best way to move your backup data to a new environment is simply to restore the tape's data archives and then extract the data. From there, you can typically easily import the content into the new environment once you've recreated the archive structure. Some backup systems even allow you to fully import the older archives completely into the new data structure.
This is not to say that upgrading and changing between archive systems is in any way quick or easy. In fact, restoring and migrating older archive structures can be immensely time consuming. Because each backup system saves data in its own way, it's important to have strong knowledge of the old AND new backup system BEFORE you begin such a process.