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.

PList list= web.Lists["MyList"];
SPListItemCollection items= list.GetItems();
web.AllowUnsafeUpdates = true;
foreach (SPListItem item in items)
{
     item["Title"] = "New Title";
     item.Update();
}
web.AllowUnsafeUpdates = false;

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.

SPSecurity.RunWithElevatedPrivileges(delegate()
{
    using (SPSite site = new SPSite(web.Site.ID))
    {
    // implementation details omitted
    }
});