New refrigerators are improved - some will de-freeze automagically, their power consumption could be reduced (thanks to ? better insulation and better compressors maybe), some will start-stop more often in order to keep the temperature in the fridge from changing too much, some have nice blue lights and so on.
A new fridge uses some 1 kWh a day. Assuming the old one uses twice that, you could stand to make a saving of 350 kWh a year, or some $35 worth. Not good... unless to fix the old one would cost you a big part of the price of the new one.