As a principal, you should always operate the device at 60 Hz. Even though your monitor might claim to support 72 Hz or more, the picture does not automatically get better with a higher value. Because the fact known from CRT monitors that a higher Hz value provides better image quality does not apply here.
But you are advised to read in the manual of your monitor which setting the manufacturer specified to be most optimal. There are actually a handful of monitors out there that were optimized for a higher Hz value.