For clarity: You can’t upgrade a 32-bit install to a 64-bit install directly, you have to either use the Upgrade Script. Even then, there are things that may not get handled cleanly - the script is good, but not all-knowing.
Once you have a 64-bit installation in place, you can (if you install FreePBX Version 15 and upgrade it to current) backup the old server (see various posts about the ins and outs) and then using the FPBX15 RESTORE function to restore the old data to the new server.
Note that this is relatively new software, so there may be a hitch in this process as well.
Finally, the ‘tried and true’ method is to upgrade by hand, use the bulk-handler (when possible) and copy the files you need from the old system to the new system. This is my preferred method, since many things have changed from the old software to the new software and some options are no longer relavant or new options have been added. For example, PJ-SIP is the preferred SIP Channel Driver now, so all of the old Chan-SIP settings that are tied to port 5060 will mess you up.