WordPress on shared hosting assumes that the end user understands how to maintain a WordPress install. The big things being updating WordPress, and even more importantly updating their WordPress plugins.
WordPress plugins are notorious for having security vulnerabilities and may result in the site being modified by a malicious party. A hosted solution should be able to respond to these issues more quickly, and remove the malicious changes, and update and/or protect the plugins.
As well a hosted solution will likely have backup systems in place as well as being hosted on high availability infrastructure and caching layers for busy sites to mitigate load to keep the amount of CPU resources at a minimum, allowing busy sites to host a lot of traffic and slow traffic sites to have the CPU needed to render their site in a reasonable (milliseconds) amount of time. These benefits come from the host knowing they are hosting WordPress and only WordPress, and thus can deploy specialised solutions.
On shared hosting one usually gets an Apache, with some random version of PHP that is decided to be good for most people, and access to a database. If your application gets slammed you chew the CPU on the host and the host will likely throttle access to CPU resources rendering the site effectively offline. This means that a hosted solution will usually be mostly impervious to a DDoS and a shared solution can be taken offline with modest resources. As well, the end provider doesn't have a way to test everyone's website with updates they are going to apply, so sometimes the host may break some sites to perform updates to the installed PHP or other supporting application software.
