<remove name="" /> ,When finished with all layouts, Magento will completely delete the block with indicated name="", regardless of which layout handle it has been added to. Using this method it is impossible to remove a block from one location and then add it to another
<action method="unsetChild"> operates only in the context where it is being used. unsetChild is created for moving existing blocks from one place to another. You need to use this method if you want to remove a specific block from a specific layout handle and then insert it to another position or layout handle.