Depends on what you want to use it for, although for most people there is not too much difference.
HDMI (newer spec and new cables) can carry Ethernet, although that is something that you probably won't use in your home PC. It also has an audio return channel for use with Over the Air television reception hooked up to an A/V system, which is also almost certainly not needed with your PC.
Displayport can carry multiple video signals (up to 4 1920x1600, with separate audio for each) and allow daisy-chained monitors (again, newer specs, in this case requiring that the monitor allow video pass-through). Displayport can also be used with an adapter to connect to VGA monitors/projectors, which may be useful. Displayport is also capable of sending a signal farther than HDMI at a given resolution, which may be helpful. Possibly more importantly, both G sync and Freesync must be done over displayport.
Displayport has more features available to it that may be important to a computer user. If these features are important to you, then yes, displayport is better. If you want to use a single "generic" monitor, then it probably doesn't matter, so long as the monitor has the same port as your computer (pretty much every monitor nowadays has HDMI as a minimum, and likely has displayport too).
Mike
