I've used HDMI for Channels extensively (and contributed to that thread quite a bit).
I think it's too soon to make a fair comparison.
Right now the HDMI solution is far more refined and reliable.
In my experience, the Chrome Capture feature has relatively poor picture quality, the video often doesn't fill the screen (it's windowboxed with borders around all sizes, this is most noticeable on a television), the app often crashes, and a good solution for authentication is not yet in place. It looks very promising going forward, but one Chrome update could permanently break this option entirely. Something to keep in mind.
As a long-term solution, the HDMI encoder setup consumes less energy (compared to a running PC encoding video) and should be way more resistant to changes in DRM (will work until HDCP is replaced). But it's a pile of hardware you have to setup, which is a big negative.
I'm interested in seeing how all of these things evolve over time. It's good to have both options.