In managed, the service provider handles server management and other security updates. In unmanaged you have full control over the server, and you are responsible for the maintenance and security updates.
Managed hosting providers optimize server performance and scalability for you. In unmanaged hosting, you must configure the server to meet performance needs.
Managed hosting is usually more expensive due to added services. Unmanaged hosting is cheaper but requires a higher skill set to maintain.
Managed hosting providers handle security patches and updates. With unmanaged hosting, security is your responsibility, requiring constant vigilance.
Managed hosting includes comprehensive support services. Unmanaged hosting provides minimal to no support from the provider.
If you need hassle-free hosting then choose managed, if you want control over your server then choose unmanaged.