The Steam Link uses your home network to connect to your PC, not the internet. It's more versatile in that it can be moved easily, use wifi, and you can connect multiple PC's to it, as well as controllers and so forth. Its disadvantages include higher latency since it has to stream video across your network, processing overhead for that streaming, and lower quality audio and video since it has to cram everything into at most a 100 Mbps connection. HDMI has something like 10.2 Gbps to play with so it doesn't need to bother with compression.
When it's an option and you won't be stumbling over the cords, I'd go with HDMI when possible. Just don't pay too much. Markup on cables is ridiculous when you can get an inexpensive Monoprice or Amazon branded cable that works just fine.