I'd do both. Post it first to your blog. Spread it on twitter/facebook/email list with a link to your blog.

Then after a few days copy it onto other platforms. Like Medium (with a link back to the original) and LinkedIn Pulse (if it makes sense for your audience).

Wouldn't that just result in duplicate content?

Are you talking about it from an SEO perspective?

If it points back to the original Google recognizes the original for SEO purposes.

You can try it, but there is a saying: "Put all your eggs in one basket and watch that basket."

Spreading yourself too thin can be a problem rather than adding value.

Best of luck.

How are you expecting Medium to add value to your posts? Won't routing traffic through Medium just shave 90+ percent of it off?

E.g. if it is the first blogpost you made. Chance are higher on medium to get it spread. Don't you think?

I think it's more likely to get an insignificant amount of readers from medium, especially on a recurring basis. They don't publish page views on posts but it's an open platform, the median post is going to get nothing but what you provide yourself.

You may end up marketing medium to market your blog to market your site which is a lot of steps for someone to take to become your user.

I actually decided to test this hypothesis if you're still around - so far the results are 80 visitors reaching my post via medium, 5620 via my own efforts.

And a second article I didn't try to promote anywhere, which got no views at all lol. It's pretty much BYO traffic.