For me it is a matter of the machine's architecture. On my 32-bit computer I use 32-bit, and on my new 64-bit computer, I use the 64-bit version to unlock the full potential of the computer's design. From what I understand, 64-bit applications use a bit more RAM but are much faster than their 32-bit counterparts.
Dell Dimension 4600i, nVidia GeForce 6300, 4 GB RAM, Linux Mint 13 32-bit, MATE edition
Dell Latitude D400, Intel Graphics, 1 GB RAM, Linux Mint 13 32-bit, MATE edition
Gateway DX4860, Sapphire Radeon HD 5450, 8 GB RAM, Linux Mint 13 64-bit, MATE edition