Transferring full database to another machine oracle 10.2 xe
You should be able to do that with an RMAN backup. You need to see what kind of backup Oracle XE supports. But you should be able to shutdown the database, startup mount, then do an RMAN backup making sure to tell Oracle where to send the backup, make sure that you include the control file with the backup. Then copy the backup over to the 64 bit server and inside RMAN use "CATALOG START WITH 'D:\backups';" or where ever the backup is. You need to copy over the init/spfile, create a service on the new server, startup nomount the new service, in rman, connect to the new database service, restore the control file, make sure that the control file restored, then restore the database. You will not need to recover the database since it was done while the database was not open.

You then need to find and run the script in %ORACLE_HOME%/rdbms/admin that will convert the database to 64 bit then upgrade the database to 64 bit. It would help if you have a 10g 64 bit home on the new server, but I was not able to install 10g on Windows 2008, it just won't install, so you probably need to run the upgrade manually. You can also upgrade as a 32 bit database on XP and then migrate the database as 11g.

Another option is to create a new 11g 64 bit database on the new server and use data pump to migrate it. Regardless you will need to test the process and probably try it more than once.