There are many advantages.
You are typically on a higher end server.. (even though you are not the only one it is a much better server then most normal dedicated servers out there)
You are on shared storage. (SAN). This provides you with a ton of data security. Your data is on a private network instead of being directly on the server. The storage will have RAID if one of the hard drives go bad, you will never notice it, If the entire shelf goes down, it usually has redundant features such as multiple controllers, and multiple disk array shelves, so even if one disk shelf or controller goes out. You will not feel it, and your data will still be there.
If a cloud host is using a software such as VMware or Citrix or Microsoft as there cloud virtualization software. It has a lot of great features to basically provide 100% uptime. It also balances out resources. If you are on a farm of 10 physical servers with 100 virtual servers, it will load balance the servers depending on server resources to make sure there is no hardware that is overloaded. If the physical server you are on, it will automaticaly migrate your virtual server to another physical server to keep it running. usually in less time then a reboot.
Some of the Cons are this.
If you run a big enough server farm. It will cost you more in the long run to be on a cloud
Some else has access to your information. If there is a rogue employee or a creep working there, many people have access to your info.. I do cloud consulting for a lot of financial firms and this is usually will have them spend the money to build there own in-house cloud then give it to someone else. Especially for compliance reasons.
PS. If there are any really big companies out there that need have a big server farm and are looking for some virtualization consulting, feel free to hit me up
I am vmware and citrix certified