The site stays at Squarespace, and the export only returns content. Its help page on exporting lists what comes out, layout pages, one blog with its posts, text blocks and image blocks, and what doesn't, other page types including store pages, style settings and custom CSS. The same page states that it's not possible to export content from one Squarespace site and import it into another. So you get your texts and images back, and the rest is rebuilt elsewhere. The domain name is a different matter, it can move with you, and my guide to domain names explains why it must always be in your name.
The shared template sets the pace for your content. Every Squarespace template is offered to all subscribers, which means the structure of your pages and the order of the sections appear on many other sites. The editor protects consistency by limiting deviations, and that's exactly what gets in the way the day your business needs a page that doesn't fit the mould, a comparison of services, a season calendar, an online quote, one page per town to be found locally. A site coded for you starts with the list of what your customers search for, and the layout follows, never the other way round.
The speed of a Squarespace site depends on what the template loads for everyone before your content. An online builder delivers the editor's code, the fonts and the scripts planned for every feature of the template to each visitor, including the features you don't use. On a recent laptop the difference is small, on a phone in a car park it shows. I'm not claiming every Squarespace site is slow, I'm observing that a site coded for one specific business carries only what its pages need. Before going live, every site I deliver passes a check on speed, accessibility and technical SEO, and I send you the result.
The displayed price leaves out the hours you put in. Core at 168 € a year is 504 € over three years, plus your hours in the editor, plus paid extensions if a feature is missing. My Essential plan costs €1,405 over three years, and that amount covers design, code, hosting, backups, updates and your text changes delivered within 48 working hours. On subscription alone Squarespace stays cheaper. The difference buys not touching the site any more, and knowing someone checks every month that it holds. To see where that price comes from, read how much a website costs depending on how it's made.