I own both (HD6XX and DT880 pro @250 ohms). HD6XX has a narrower but more accurate soundstage and has slightly lifted midbass, DT880 is more spacious sounding and has a bit more treble (around 8k). If you're young and your ears are still sensitive to treble, HD6XX might be a good choice. If you're over 40 and your ears start to lose sensitivity to high freqencies, you might appreciate the little extra treble from DT880. But differences are not that big imo, both sound reasonably "flat" and you'll be fine with either, regardless of age ;)
I don't own the ATH M70x (I do own ATH M50x, HD6XX and DT880 are better for mixing imo), but they're closed back and those usually sound less "flat"/accurate than open backs. ATH R70x might be a better choice, I've heard them for a minute or two at an audio show and they seemed pretty accurate/"flat" at first listen.