the 780? not sure why your asking since its obvious which is better..
4GB DDR5 is for multi monitors. 3GB DDR5 can do well with 3.
780 has better GPU, more cuda cores. 780 pew pew's all 770's and has better fps results. Why would it cost 150$ more than 770 then? Also it consumes 10W more wich is like nothing. If the specs say so, It's like an old car with best engine and all the stuff and a ferrari wich is like 780. Go for 780 trust me, you won't regret.