There are actually 4 versions of the DT 880's: 32, 80, 250, and the older (harder to find) 600's. (I don't think you can get the 600's new any longer though.) The 80's definitely have more low end, but I've seen that the others, the 32, 250, and 600, all have more or less the same sound signature.
I have the DT 880 250ohm model. At first I loved them, but over time they got harder to listen to, because of their piercing treble. So that is definitely a concern for the 770's! I like what you say about the Meze's though. I just need to somehow satisfy myself that the low end won't be too overwhelming.
How did you find the lows/mids of the Meze's vs the 770's?