TDB runs on both 32-bit and 64-bit Java Virtual Machines. The same file formats are used on both systems and database files can be transferred between architectures (no TDB system should be running for the the database at the time of copy). The difference is that a different file access mechanism used.
The file access mechanism can be set explicitly, but this is not a good idea for production usage, only for experimentation - see the File Access mode option.
On 64-bit Java, TDB uses memory mapped files and the operating system handles much of the caching between RAM and disk. The amount of RAM used for file caching increases and decreases as other application run on the machine. The fewer other programs running on the machine, the more RAM will be available for file caching.
TDB is faster on a 64 bit JVM because more memory is available for file caching.
On 32-bit Java, TDB uses it's own file caching to enable large databases. 32-bit Java limits the address space of the JVM to about 1.5Gbytes (the exact size is JVM-dependent), and this includes memory mapped files, even though they are not in the Java heap. The JVM heap size may need to be increased to make space for the disk caches used by TDB.
The on-disk file format is compatible between 32 and 64 bit systems and databases can be transferred between systems by file copy if the databases are not in use (no TDB or Fuseki instance is accessing them at the time). Databases can not be copied while TDB is running, even if TDB is not actively processing a query or update.