I have the A900X my self and I been enjoying alot and I listen to Daft Punk as Dubstep, Drum n bass and as well Ambient, IDM and other forms of Electronic music, as well as Jazz and classical, I do dip in rap once in a blue moon and I found they did a good job with that as well. I had mine for close to a year so they burned in. I do use the A900X for gaming as well and to me they work very well in gaming, since i able to keep them on for hours now that the earpad broken in.
I'm not good with giving a good explaining on how they sound with those music. But to me they do a very good job with music I listed, The bass is perfect to me, its there when the music calls for it and isn't when the music doesn't,I don't listen to metal or pop so I don;t know how those sound on the headphones. The 3D flaps on the headphone doesn't bother me at all and feels light on my head. The rubber band mod works with these headphones where the rubber band makes the headphone tighter on your head. So it doesn't slide off if that does happens to you. The ear pad's doesn't really bother me and my ears fit inside of them easy. But I seen people mention that there are other earpads from other models, that will fit on them.
The A900X is fairly easy to drive so you do not need to plug them into a headphone amp, The cable of the headphones is very long but the cable is braided. I dropped mine a couple of times on my desk and they still in great shape. Also if your source is not good, the headphones like any other type of good headphones will bering out the flaws of your source.
I don't know any thing about the DT770 since I never used them so I can't help you there.