The reason for introduction of Sandboxed Solutions was giving ability to work on a partially trusted environment. Without disturbing the Farm Administrators, the Site Collection Admin can handle the deployment. This runs under a set of security policies said CAS Policies. Also with this Sandboxed solutions come under several limitations.
Here are some Considerations on choosing Sandboxed Solutions. Also here are some restrictions on it.
Even a farm solution can be managed to deploy to a particular site collection if needed and the control the sites where the features get activated. Now with SharePoint 2013 and Apps comming in Sandbox solutions are considered obsolete. Still not dead.