It's not quite that simple.
As Walt Mossberg wrote, the intersections between the two are becoming increasingly blurred with supposedly closed platforms created using ever more open technology and platforms hailed as open being built on proprietary code. This position is seen by some as not a true reflection of the open vs closed argument, that it is the end result that counts rather than any of the technologies employed.
Supporters of the open web call for standards allowing for interoperability between services, for movable data that can be housed in different systems because they all talk the same language.
Writing or publishing
Some just want to write and are not bothered about retaining control over the results or in owning their own domain (unlike 10 years ago) which is no doubt a response to the social web where we endlessly pump out our thoughts - largely for the good of the platform. They just want to write and not to publish.
Some see the upkeep of their own site as prohibitive, others decry the lack of network effects available to a blog on an increasingly social web. Even more just want to write and feel that services like Medium provide an environment where they don’t have to exert any other time and effort to getting their words out - the literary equivalent of Mark Zuckerberg's wardrobe.
There is no doubt that writing on Medium has become fashionable, it has rapidly become the de facto standard for politicians, business leaders and celebrities. Now, people who might otherwise have considered starting a blog, or even those already with their own sites, look at what is happening and feel that if they put their words on a service which is seen to be synonymous with quality writing that they will instantly find an audience – a lot are realising that this isn’t the case.
Platform or Publisher
With Medium being both platform and publisher, with increasing aspirations towards the latter, there is a renewed hope that writers might get paid but the likelihood of this happening for the individual not attached to any significant publication are currently slim. Maybe this will change in future.
But the historical bastions of the closed web are starting to open up allowing for cross-posting by way of open systems; they may not be standards but they are the next best thing. These new tools, such as Facebook Instant Articles and the Medium posting API enable a "post once, publish many" environment allowing for the best of both worlds: local control coupled with enhanced distribution.
Because of this, we are almost heading full circle.
Blogging was previously the only option for most to publish their thoughts but the growth of the social web and its proprietary platforms made many (myself included) feel that they had to go to where the audience was.
Now, however, these new tools have started to negate those effects and the need for people to abandon their blogs. Now, we can write in our own space but take advantage of these platforms with no additional effort.
Frictionless movable data.
Modern platforms may seem like the new pillars of the internet, giant 2001-esque monoliths impervious to time and change, but platforms have died in the past. Do we want our work to die with them?