I'm currently setting up my blog and I didn't even hesitate to host it myself. Companies like Medium come and go (e.g. Geocities, Xanga, Myspace, Posterous), but your dot com is yours as long as you keep paying the domain fee. Guys like Scott Hanselman and Jeff Atwood are probably very happy they've kept their presence on their own dot coms over the last decade.
Wow! I never really thought of Medium in the same realm as Xanga or Livejournal but you're absolutely right. It's crazy to think that people are moving to it. LiveJournal and Xanga were always kind of a stepping stone back in the day. You had your blog on their first then it started getting a lot of traffic and you moved it to your own domain. It's crazy to see the opposite happening now adays with Medium!
The big difference is that you can point your own custom domain at Medium, and if you want to leave, you can move your posts to your own site and maintain the canonical url structure.
I hate Medium and I wouldn't let them be my primary distribution method for content but I would dual post. Is there a reason why you wouldn't just xpost from your blog to Medium?
SEO mostly I guess. Like medium already has a very high page rank or domain authority, so the medium's post comes first in search results.
Also, Google probably considers having duplicate content as plagiarism and your blog might rank low. The alternative may be post on your blog first, then post on medium in a couple days.
Medium allows you to setup canonical links. According to Google, that means the original post will be ranked highly when more than one instance of the same content is identified. Or does it play out differently in practice?
Would love to see actual data or even anecdotal examples of what happens when people crosspost to Medium and properly setup canonical links.
The problem I've seen is that canonical links aren't always effective -- I've seen sites get published for duplicate content even when they're used. There's horror stories posted in Google's forums; hate to become one.