All the configuration and data files are the same on i386 and amd64. The same procedure for transferring the site to another server would work just fine here.
Make sure you backup the existing system. Verify that backup! Making two backups isn't a bad idea either. Exporting a list of the ports you have installed is a good idea too (
pkg_info -ao | grep "/" > PkgList.txt or similar).
Depending on what version you're running now, and exactly what software, you may be able to in place upgrade to the new version; just install the base and kernel. Sometimes that's enough, usually you have to rebuild the ports for the new libraries (
portupgrade -af after installing the portupgrade port). If you want to try this route, I highly suggest using one of your backup copies to try this on another machine before doing it on the live server.