the main advantages of the 64-bit architecture are
addressable memory size from wikipedia:

# Memory mapping of files is becoming less useful with 32-bit
architectures, especially with the introduction of relatively cheap
recordable DVD technology. A 4 GiB file is no longer uncommon, and such
large files cannot be memory mapped easily to 32-bit architectures;
only a region of the file can be mapped into the address space, and to
access such a file by memory mapping, those regions will have to be
mapped into and out of the address space as needed. This is an issue,
as memory mapping remains one of the most efficient disk-to-memory
methods, when properly implemented by the OS.

# There may be other incidental advantages as a result of the
transition - for example, in the case of x86-64 compared to x86, twice
as many registers are available for programmer use.