VPS Hosting Pros
1) The cheapest of all web hosting options that allow full root access and provide an option to install and use any own server-side application of your choice.
2) While the hardware resources are still shared between users, typically there are way fewer clients sharing the same server, allowing much greater CPU and RAM usage.
3) Does not require maintenance of the network, including uptime monitoring, very basic DDoS protection and general network security.
4) Does not require maintenance of the server hardware.
VPS Hosting Cons
1) Requires maintenance of everything software-related. Basically, you are being provided with just hardware, and installing and maintains everything else – the operating system, the web, ftp and mail servers, database and other applications is up to you.
2) Hardware resources are still shared – even though in a different way (virtualized, or in other words – isolated from each other) – the available CPU and RAM might not be enough for your needs in some cases.
3) In some very rare cases certain server-side applications might have issues running in a virtualized environment.