As
@GREQ said above,the Sextetts have fantastic mids,which is important IMO for rock and metal. Ive read about many members here who dont care about mids for rock,and frankly,I dont understand that,but whatever. Since you dont like the DT770s for rock,it sounds like the Sextett would be perfect for you,as theyre very different sounding from the Beyer.
The Beyer is a more dynamic sound. Lots of treble and bass,with crap mids. It sounds bright.
The Sextett is a warmer sound,with phenomenal guitar and vocal sound.
There are three different versions of the Sextett,and it can be a bit tricky to not only find a pair of Sextetts vs. other other headphones named K240,but also to know which Sextett you are getting. I have all three versions and prefer the MP. The EP is good too,but if youre into fast metal(black,death,melodeath) i think the bass of the EP can get in the way. The LP im not too crazy about personally.
Finally amping the Sextett is no joke. I have no idea about your NAD on whether or not it can drive the Sextett well. I have tried several different amps,both solid state and tube and I prefer vintage solid state receivers for the Sextetts. All my other headphones I use a tube amp for,but the Sextetts+receiver= magic to my ears.
Finally,unlike Greq,I do not think the Sextetts are overrated,nor overpriced. I own headphones that cost thousands of dollars and I still use my Sextetts for rock and metal often. For the price,I think theyre one of the best bargains in this hobby.
If you havent yet seen my videos on the Sextetts and using receivers as amps,here you go. Let me know if you have any other questions.