>DisplayPort
+ Higher bandwidth (DP 1.4, 2.0)
+ Can daisy-chain monitors
+ Locking mechanism so it doesn’t unplug easily
+ Better for high refresh rate gaming (144Hz+)
- Not common on TVs or consoles
- Cable length limits for full bandwidth

>HDMI
+ Works on basically every TV, console, projector
+ Carries audio and video easily
+ HDMI 2.1 allows 4K 120Hz, 8K
+ ARC/eARC for audio return in home theater
- No daisy-chaining
- Older HDMI versions have low bandwidth
- No locking, can unplug if you sneeze on it

>tl;dr
Use DisplayPort for PC master race monitors, HDMI for normie TVs and consoles.