The tranny is definetely stronger. You should pull that and send it to me...
Really, outside of the drive train not much else will bolt up to the 77. But seeing as you have a 81 I would pull the glass, dash, heater assembly and whatever else is worth while just for extras for the 81. I'm stripping down an 83 for my 81. The 83 is in horrible shape, but a lot of the parts are good so to save some money I'm keeping everything I can off it.