Hi sainteb,
You mention both, both imo are very similar but not the same, both dt's have the basic Beyer house sound, ie slightly v shaped, sparkly highs, powerful bass, slightly recessed mids, the original dt 770 is the brighter of the two, it has similar levels of detail compared to the 650, it will also, at first seem much brighter, bass is deeper too, also both versions, for closed back, have good soundstage, almost equal to the 650, the 1770 is similar but maybe a bit more refined, slightly smoother highs compared to the original dt, a bit less sparkly, mids are still slightly recessed but very detailed, bass is deep tight and slightly warm, the 1770 is quite a bit more costly than the original though, I have owned both but I sold my 1770's because I didn't think they offered me much more than the cheaper originals, and kept my original 770's, if you like the warmth of the 650's maybe have a look at the 1770's, if you fancy something brighter, then perhaps have a look at the 770's, either way, imo you will be getting an excellent se of cans.