Heya,
I have both and I have to say, the D1100 sounds like a metallic tinny sounding weird headphone. It's treble is just weird. It's like it has some weird spikes and just sounds really robotic or synthetic. It's not warm and musical to me at all. The DT770 on the other hand, while bright, has a lot warmer signature to my ears and sounds less like a strange unnatural sound. Bass was pretty similar on the two, both can hit hard and low and are great for bass. Both isolate rather well. Massive bonus points to the DT770 for comfort (velour pads) and style. The D1100 is one of the ugliest headbands in existence. Also size of cups are larger on the DT770 and feel more spacious. Sound stages are good on both. Between them, the DT770 simply is the superior headphone. The D1100 can fold/flex a little more so is a bit more portable, but with how it sounds, I'm unsure how it carries the price tag that it does.
Check out the HTF600 if you want bass+soundstage on a dime. Fantastic headphone.
Very best,