The primary reason I’m looking for an alternative to WordPress is its reliance on PHP. A language so awful I wouldn’t let it anywhere near my computer if I didn’t rely on WordPress for my blogging. Using PHP as the substrate for your CMS/blogging platform guarantees you’ll have day one security problems. Just look at all of the WordPress plugins and themes that have horrible security flaws (e.g., revslider).
If you don’t have a design muscle in your body, you might experience some difficulties making a Squarespace site look good (due to the platform’s reliance on good stock imagery to be part of your site’s final look). Also, Squarespace offers a good range of features from the get-go, but above that, there’s not much you can do when there’s a feature missing. Just like with Wix, if you want a site that can grow alongside your business, this might not be quite the solution you’re looking for.