One of the example of self-hosted is WordPress.org and an example of hosted is Wix.
Self-hosted enables you to have complete customization over your website or blog vs hosted come with a handful of limitations including speed, features and customization. The differences are summarized. Considering all the differences, the website in self-hosted environment would work more efficiently.
Popularity and technical Support:
Self-hosted like WordPress powers over 30% of the internet which makes it popular and demonstrate a high number of users and therefore many support from software engineers to improve it through updating and optimizing the WordPress by adding more features as well as enhancing the functionality by developing more plugins and finally have more established support from the community as many people use WordPress to make their website.
Choice of theme:
Self-hosted enables you to access to over 11,000 different themes. It enables you to upload third party themes to increase customization for backend vs for Hosted only limited themes options are available within the platform.
Choice of plugins:
Self-hosted enables you to access to over 50,000 different highly efficient plugins, vs hosted are limited and also not having very functional plugins as numerous options available with WordPress.
Self-hosted enables you to upload plugins to increase functionality for the backend to facilitate designing a website (e.g. Elementor for WordPress).
Own domain name:
Self-hosted enables you to own your unique domain name vs hosted do not for instance (yourwebsite.wix.com) unless to upgrade to the premium one.
Upgrading to Wix premium website in order to have your own domain name cost more than self-hosted web hosting options available out there.
Monetize the website:
Self-hosted enables you to monetize your website Ads which with hosted you are not able.
SEO control:
Self-hosted enable you to take control of your SEO while hosted one do not that much.