My favorite podcasts have all started raving about Squarespace---and, more to the point, offering codes to save a few bucks---so I gave it a try after having a self-hosted blog at Wordpress.org for years. I liked the way the templates looked and worked, and the domain mapping was pretty simple. The import worked perfectly, including comments, plus you can easily match the URL mapping schemes between the two services, so I took the plunge and paid for the account (you get 2 weeks free, but you don't get the domain mapping unless you pay, and that was a major part of what I wanted to try). It costs $8 to $10 per month for a basic account, so after I removed the site hosting fee for my self-hosted blog I landed about even. If you're reading this, you're reading it on Squarespace, so you can see how it looks. I like it. But Squarespace has some issues.
The templates are all nice-looking and nearly endlessly customizable without the necessity for mucking around with custom CSS (although you can) and the horrifyingly endless and confusing screens that Wordpress themes typically have. The nuts and bolts of bloggery are seamless: write a post, tag it, categorize it, and bam. You're good to go. Creating nice pages with multimedia is extremely simple as well; see my pit bulls page.
The gallery feature is handy, and it syncs with a mobile Squarespace Portfolio app that pulls down gallery pics into an iOS app. It doesn't allow adding photos from a mobile device, which is a serious shortcoming (in fact, Wordpress wins hands down as far as mobile blogging), but the viewing is really stunning. You can e-mail photos to galleries, but a GUI interface would be nice.
Squarespace allows you to post in Markdown, which I love. It even has that as a preference in both the Web and mobile interfaces. Now I don't have to write somewhere else and export the HTML to post to Wordpress. Paper the world in Markdown!
Their customer service is as good as the podcasters say. Unfortunately, the reason I know this is the multiple problems I had, including the horrifying shortcoming that sitewide, Squarespace RSS feeds don't work with IFTTT and multiple issues I had paying for my account. But a human answered each of my e-mails within 30 minutes, and in the case of the IFTTT issue when they couldn't do anything about it, they were very apologetic. I would rather have a broken feature or two but the assurance that someone is going to try to help me when stuff breaks. Just try getting help with a Wordpress problem that isn't covered in the forums. It won't happen.
The drag-and-drop templates have a few unintuitive quirks that frustrated me quite a bit. Squarespace works with blocks, which you fill with predefined types of content (photos, videos, code, etc.), and then you drop the blocks on a grid. Sounds simple enough, but the blocks don't fall easily on a grid about half the time. If you have a long block of text, you require an act of God to put a block above it. If any scrolling is required, you'll want to tear your hair out.
Squarespace has mobile apps, but anything other than plain text is not possible or, at least, not easy. The iOS app does have stats built in, which is nice, but overall the mobile apps are frustrating and lack features.
I don't see anything to rival the numerous widgets that Wordpress has. Squarespace has the blocks to drag and drop, and they cover the very basics, but some functionality is missing. For example, I would like to show recent comments and the most-read posts. It does have a code block, so I may be able to find a way to add those things that way, but it's not as easy as Wordpress.
I'm also bitter about the RSS issues. It's not even easy to figure out the feed for your site, and although it works with Feedburner and Twitterfeed, the inability to use it with IFTTT is irritating. RSS is not dead, and I think Squarespace really underemphasizes it.
I am happy overall. I need to explore a little more. Perhaps some of my issues can be solved. I think that particularly for people who are new to blogging, Squarespace is a clear winner. You even get a domain name for free if you don't already have one (although, irritatingly, if you DO already have one, you cannot transfer it). They offer a 2-week trial, and you don't even have to supply credit card information to get it, so there's no reason not to give it a try.