Originally Posted by Often1

If you misconnect due to a late arrival, the rebook will be BA's responsibility and EC 261/2004 will apply. Thus, the hotel (if one is required) will be courtesy of BA. If BA is ontime-ish and you misconnect for other reasons, e.g. delays at CBP, AA will nonetheless rebook you onto its next available flight. Around the holidays that might be far from the next flight. The overnight would be courtesy of your bank account.