Yeah I own both of these cans. The DT770/80 is a good solid pair of closed headphones for the price, but because it's a closed design and whatever else, it cannot compete with the HD600 properly amped with upgraded leads for sound quality. I use the DT770 mainly for isolated listening and some specific music choices.
If you're still going down the unamped/cheaply amped road, then of the two the DT770/80 is probably a good bet if you want closed phones, but if you don't care about isolation then there are many other choices in that price range, e.g. HD580, MS-1, Grado SR-125/225 etc. I am more of a lie in bed, close the door and relish-the-music headphone listener, so the HD600s and SR-325s suit me fine for 95% of occasions.