The HDMI cable would be the simpler choice.
Steam link is only as good as your internet connection so if you have good speeds then you shouldn't have a problem.
Steam link also gives you the option of moving it to another room so you could game in any room in the house.
Also your not limited to just steam games you can stream anything with the STEAM LINK https/www.youtube.com/watch?v=LaN_A8m9RnA
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.
Steam link works well but you need to be hardwired really (or home plug/powerline) - I had dropouts & artifacts wirelessly even with a 80meg good signal.
Limits - 1080p & 2 channel audio.
Expensive option unless you're going to make the most of it - I use it simply because my gaming rig is upstairs & it allows me to play on the 60inch downstairs tv when I feel like it.
As said you can play any software through it though , just add a shortcut to the steam games list.