I've moved this website from Wordpress.com over to Squarespace.
Advantages of Squarespace
The advantages of Squarespace over Wordpress from my point of view are flexibility, the control over design aspects, security and customer service, and ease of setting up ecommerce. It's not free but I think those things are worth paying for.
As an editor specialising in technical writing and plain English, I found the Terms and Conditions at Squarespace refreshingly readable and easy to understand.
Comparisons with Wordpress.com
Wordpress.com and Wordpress.org
Wordpress.org is the self-hosted wordpress option - you have to install it, install plugins, do the upgrades for the software and plugins, and you are responsible for security. You can assume that people talking about Wordpress are talking about Wordpress.org unless they specifically say Wordpress.com.
Wordpress.com is free, relatively easy to use and flexible, and the security and updates to the software are all taken care of by Wordpress so you don't have to worry about whether you've installed a dodgy plugin or one that's not supported by the current version of Wordpress. However, if you want control over design, you have to pay to customise a template, or pay for one that has the features you want. Also you have to pay if you want to remove ads.
Squarespace and Wordpress.com
Squarespace was recommended to me as an alternative that will allow much greater control over design, and also has the security taken care of for you. I've been looking at comparisons of Wordpress.com and Squarespace.
I found a useful comparison of Wordpress.com and Squarespace (it also compares wordpress.org but I wasn't interested in that).
Options for ecommerce
The same site has an 'essential guide to choosing an ecommerce platform', which compares options such as squarespace, a Paypal button, and Etsy. It also talks about Wordpress.org and ecommerce.