Is the new Unity server part of the same directory (domain) as the old one? If you're creating a whole new system in a new directory you can use DiRT backup and restore to do that.
http://www.ciscounitytools.com/Applications/Unity/DIRT/DIRT.html
If they're in the same directory then yes, GSM is fine - typically you'd use GSM first and then you can do a COBRAS backup and rstore it to the same system which will pick up your call handlers, interviewers, schedules and such and update the users you moved over.
If they're in seperate directories you can just use COBRAS for that if you like:
http://www.ciscounitytools.com/Applications/General/COBRAS/COBRAS.html