HDMI is a great technology, but if you have to run the cable over long distances they're not the most reliable. Ethernet cable (or, more correctly, Cat5e/Cat6 cable), on the other hand, is better ...

Some (many?) HDMI cables can also carry Ethernet over HDMI. The main use seems to be to provide internet connection to a smart TV from a cable modem box. Currently I have an ethernet-USB adaptor ...

Bi-directional audio means that a single HDMI 1.4 cable will support an audio return channel (ARC); that could be useful if you wanted to route audio from the TV tuner integrated into your HDTV ...