For PC users who like to play games, the answer is easy: DisplayPort. Most graphics cards are optimised for this connection and synchronisation technologies such as G-Sync or Freesync also only work via DP connections.
In home cinema, on the other hand, there is no way around HDMI. Blu-ray players, consoles and set-top boxes all use this standard. This is not least because HDMI offers features such as ARC support, the transmission of input commands via CEC and the transmission of Ethernet signals. For all PC users who are not hardcore gamers and who are looking for a new monitor, the answer is: both are possible. As long as your own computer has the respective connections, both monitors with DisplayPort and those with HDMI connections are a good choice. If you want to be on the safe side, you can opt for a model that has ports for both connectors.