All I know about medium is that it won't render in opera mini which I use on my phone for speed and battery life. I know I have no excuse if I don't use a "modern" browser so I can't complain. But still, for a site that just displays some text with inline pictures, I wonder why they couldn't deliver it with some simpler tech.
Their scrollable container gives me problems with my graphical browsers. There are ways that I can get it to work (enabling JS, disabling CSS, or plugging in a mouse and using that), but I usually just load it in a text browser or pipe wget into some filters instead. For a site that is just text on a page it sure is complicated.
Qz is another new site that's horrible for just reading text out of the box. Half the time I get redirected to some other article or the front page (!?) while scrolling down or just having the page open in a background tab and not doing anything, scroll is something proprietary and doesn't work most of the time, entire thing is clunky and slow.
Thankfully, disabling Javascript actually helps a lot there.