Thanks so much for reading, matthew.bryant!
I think where content lives is a personal preference and depends on what your end goal is. I know some writers keep content separate — they prefer to write on their own blog and Medium, but not cross-pollinate the two. Others only write on Medium and don’t have a personal site all, or only use their personal site to link back to their Medium articles.
If your goal is to build a following, I would suggest having both, and make sure your Medium posts are represented in some way on your own site. (Either publish the entire article in both places or include a heading and a link on your website back to Medium.)
I prefer to post on Medium and then two weeks later publish the full Medium piece on my own blog, with a link at the bottom back to the original article. (I change up the images and occasionally tweak the text slightly if I find certain sentences could have been better phrased.) When I send out my monthly newsletter I usually include a couple of links to my articles on Medium, and the rest of the links to my blog. I do this because not all of my subscribers are Medium members, which means they’re limited to the number of locked articles they can read a month. By using both Medium and my own site, I’m able to reach people who only know me through Medium as well as those who only follow my blog.
This was a long response, but I hope it makes sense! And know this is just my opinion — at the end of the day, there aren’t really any wrong or right answers. It just comes down to what your personal writing goals are.