Finally, it took me a year to complete the HD 6 series journey, 660S,660S2,600,6XX. Must say 6XX is my favorite by not so small a margin. My preference goes 6XX > 660S ~ 660S2 > 600.
I would say of the bunch, the outlier is HD600. Although it has sweat solid mid and treble, its lack of bass is just too obvious. The overall bright presentation makes it hard to estimate the sound stage. It's probably because of this, I find it confined and veiled. Dare I say, I can't get used to and don't like it.
For general music listening, I think 6XX, 660S, 660S2 are mostly similar. If one doesn't do AB comparison, the 2-5k dip in 660S(2) is not obvious. And even with AB tests the extra bass extension in S2 is hardly noticeable. However, the smoothness in 6XX is truly something. I knew 650/6XX is known for this. What surprised me was that there is no loss of details at all. It is true though there is not much airiness compared to 660, but the space is filled with sound that should have been there, and you get that sense of fullness and completeness to make it feel real. It is smooth as it ought to be, and it is not artificially smoothed or weakened. I kind of want to question should a headphone even sound airy in the first place. I do find 6XX's treble is not as biting as 600, but it is not as laidback as S2. Among the bunch, 6XX has the least amount of sibilance. It is simply amazing they could achieve that without hurting treble performance.
Their differences are a little more important to me when it comes to podcasts or vlogs as I spend hours on those every day. The 2-5k dip in 660S(2) makes them sound like people are holding back breath when they speak especially for males with deep voices. The HD600 is even worse as it is just bright overall. With 6XX, finally people are talking normally.