Is it more efficient to have a through-the-door ice dispenser or to not have one and open the freezer door to get ice?

Unfortunately, there is no definitive answer to this question, because it depends on how often the refrigerator door is opened and how much ice you are consuming.  However, for the typical household, using plastic ice trays is the most energy efficient option--assuming that efforts are made to keep the freezer door closed whenever possible.  In most cases, an internal icemaker should also be more efficient than a through-door-icemaker.