AllowUnsafeUpdates VS RunWithElevatedPrivileges

AllowUnsafeUpdates: If your code modifies Windows SharePoint Services data in some way, you may need to allow unsafe updates on the Web site, without requiring a security validation. You can do by setting the AllowUnsafeUpdates property.

For detail click here AllowUnsafeUpdates

RunWithElevatedPrivileges : There are certain object model calls model that require site-administration privileges. To bypass access-denied error, we use RunWithElevatedPrivileges property when request is initiated by a nonprivileged user. We can successfully make calls into the object model by calling the RunWithElevatedPrivileges method provided by the SPSecurity class.