Jekyll is well suited for users who would like to have all content within source control (Git) along with the code used to produce the website. Because everything it produces is static assets (HTML, CSS, etc.), sites created with Jekyll are super fast, with very little needed on the server side of things. There are also a few really great free solutions for deploying and serving Jekyll websites. Jekyll will be tough to maintain for users who are not web developers, comfortable using Git to update content. There are 3rd party solutions for maintaining Jekyll-based sites without having to touch the code, but this will cost extra money. Also, because there is no server-side language, you will need to look elsewhere to handle things like contact forms.
If you are vanity publishing and just want to see your stuff on the web, it is very, VERY easy to get involved with. Of course, your writing is not likely to stand out if you don't have a clear plan. The more I use it, the more I like it. The user interface is extremely well-done. I kinda wish my WordPress-based blogs had editors that were that easy to use.
Straight out of the box, Jekyll lacks a friendly WordPress-style back-end. You'll be working in Liquid (HTML), Sass (CSS), and Markdown (content) files. If you're already comfortable with these languages, you'll feel at home in no time. If not, you may need to consider getting someone else's expertise to set up the site, and then use another back-end (probably paid) to make editing your site's files less intimidating.
If you use GitHub Pages for the free hosting, be forewarned that GitHub only white lists a few plugins for their own compilation. This usually isn't a problem (you can compile on your own computer if need be), but can be annoying at times.
It can be harder to get your content seen as medium is a popular platform.
It is still early days for us to track back success (traffic, rank etc) from posting to medium regularly. I hear tracking success outside vanity metrics can be hard for others too.
I am yet to figure out how to create and add to magazines - these have the potential to be a good audience booster, but not too clear.
We found the support desk of Medium to be really good. They are very focussed on customer service and are willing to go all out to help in every way they can. They are fast to respond and they are also very knowledgable at what they do. They know the importance of being customer-focused.
All the other CMS's I've used try to make it easy for the nontechnical user to manage a website, at the expense of adding complexity and weight to the system. Jekyll takes the exact opposite approach, eschewing all unnecessary complexity. If you know what you're doing in a code editor, Jekyll will probably feel like a breath of fresh air to you.
Medium is easy to use. It is easy to add highlights and emphasis in paragraphs. It is easy to add images and videos anywhere in your articles. It makes article writing fun and easy to share. Other products were more cumbersome and awkward to use or were more expensive to operate.