Like jaryd said, it's open source, which makes the biggest difference: Ghost can be hosted on your own server where Medium can only be used on Medium's servers.

Which is a huge deal for some people (myself included). I don't really trust other services to remain around, especially when doing so might put my content at risk. I'd much rather be in control of where my content's hosted, even if it means I need do some of the more fidly management and setup things.

For starters, it's open source!

https://github.com/tryghost/Ghost

That's a good start! I guess I wonder how much the uptake will be for a broader audience who can get WP for free and may not care as much about the customization experience.

The biggest problem with that is a huge portion of the WP audience is using whatever cheap shared hosting they can find, which is great for WP, because PHP and MySQL are ubiquitous when it comes to shared hosts, but Node (which is what Ghost uses) isn't.

Using Node, while something the developers probably liked, might not have been the best decision because it severely hinders adoption by the casual users that WP currently owns.

For one, you don't need to sign in with Twitter or Facebook... that's a huge advantage right away! Its also open source, which is a giant win.

The cozy sense of ownership 'cause it's open source and not proprietary.

Personal branding.