So far, what I can tell is that Middleman provides a more efficient workflow than the database-driven CMSes I have used in the past.
Jekyll has a very simple, convention driven feel to it. Templating is based on Liquid which can be a limitation in some cases.
Middleman feels more like Rails for static sites. Out of the box templates are ERB, which is messier but more flexible than Liquid.
StaticGen.com is built with Middleman, and that made it easy to add a Github extension that would pull in all the repository statistics from Github during the build and make this available to the views.
I must admit, one thing about Middleman that makes me roll my eyes is the use of "Hand-crafted" in the description of the project.
[1] https://github.com/icambron/isaaccambron.com/blob/master/con...
Ironically the folks at Meteor have pushed this approach the most: https://www.discovermeteor.com/blog/three-middleman-hacks-we...