Very good sound quality and more balanced than the Beyerdynamic DT 880 Pro I was using until now (although the latter are semi-open). The only reason I don't give 5 stars is the unacceptable fact that the headphones do not come with even a cheap EVA case like, for example, Bose or SONY headphones.

I was missing only the HD660s2 from the entire HD5 and HD6 series, now I am their owner and after several hours I now have an opinion.

The HD600 remain the best in vocals, bringing them close and making the instruments smooth in the background, they have the smallest soundstage with an amazing experience inside your head.
The HD650 are the warmest, the most calm and relaxed, perfect for bad recordings and electric guitars.
The HD660s have a larger soundstage, better imaging, better separation and now the vocals are more behind so they can breathe and come out in front, and the instruments are more enthusiastic and lively (in exchange they lose the Smoothness of the 650, 600, 660s2).
The HD660s2 are expensive, they are the 660s with additional low end that you can hear in specific parts where it goes down, they have become smoother up high, losing the liveness of the 660s but having the smoothness of the 650 and 600, they are more calm without losing the resolution and the very good technical elements of the 660s.
Fortunately, all HD6 have the same sound signature and if you don't have them side by side, I'm sure you won't notice huge differences, so those who say that one model is great and the other is terrible simply is not true.
Now for friends who are into gaming, the best are the HD 660s.
I can't say which is the best headphone, they are all great and it's purely a matter of taste.
Technically, the entire series is superior to the HD5 series. It is also superior to the Massdrop HD58X and HD6XX, the 58X are the best value for money and have drivers from the HD5 series, the 6XX are like the 650 with a darker tuning, a lot of midbass, and indeed in fast songs they show their weakness and many say they are Muddy (the 650 are warm but certainly not Muddy).

And remember that the journey to discover the best headphone has nothing to do with the headphone but with your personal taste.
I hope I helped with your choice.

Because it is a new model that has caused a "buzz" and you might be considering it, I decided to share my initial thoughts while they are fresh.
First of all, the packaging left a mediocre impression... Very simple eco-friendly box... The case is a cloth bag (??!!) But it contains all the cables you need: single-ended, balanced, and converters. The headphones have a "special weight" but they are not heavy. They are black, made of high-quality hard plastic with a satin finish. They are really enjoyable to hold. The cables connect from the bottom and you are ready for listening. I only use the single-ended cable since I don't have a balanced preamp.
The first time I put them on, they felt tight and the earpads seemed uncomfortable, even though I was used to my old (also Sennheiser) HD580. It was just the beginning. After the first few minutes, nothing bothered me. Absolute comfort. It lasts for hours. I don't know what will happen in the summer with the heat... I will probably switch to IEMs.
Now, onto the important stuff. They sound almost excellent - for their price. Yes, they may not be hi-end like the top Audeze, Focal, etc. that I have heard in demos, but they come close. Specifically:
1) There is now bass! Something that was missing in the previous HD6XX, only some harmonics. It is deep, tight, controlled. The engineers at 'S' did a great job with the new large and fast drivers they use. They didn't just talk about it.
2) The mids are detailed, pleasant, fluid, with articulation, greatly favoring vocals, acoustic guitars, etc. The 'S' has always excelled in this area, now you feel that they have taken it even further.
3) The highs are extended, natural, airy, not at all annoying, metallic, or sibilant. I would say that the mids and highs are the best in the series.
Overall, there is naturalness in textures and tones, quietness, detail, and resolution. It is not dry or surgical at all. Everything comes in a natural (maybe I'm repeating myself), airy, and effortless way when you wear them. The transients are absolutely satisfying. What is lacking a bit is the soundstage. The instrument placement and stereo image are correct, but the soundstage is close to our ears and compact. Here, the more expensive headphones will definitely excel.
I must warn you that driving them is not an easy task. Yes, the impedance has increased to 300Ω from the 150Ω of the previous models (the manufacturer claims that they are easier to drive), but it's not like that. My desktop DAC, the Pro-Ject Pre-Box S2 Digital, struggles to reach satisfactory levels at 70% volume. The same goes for the Chord mojo (v.1), it is literally in the red and the battery lasts for only one album! To give you an idea, the old HD580 and a borrowed HD600 required 80% volume on the Pro-Ject for the same level (and of course, no bass, huh?). So, in this aspect, things haven't improved much. If you don't have a headphone amplifier/DAC that "has power," you might be disappointed.
Finally, I want to tell you that in the online media, you will read many conflicting things and perhaps over-analyses from the experts. Personally -I consider myself a music lover first and foremost, then an audiophile- I believe that Sennheiser probably took what they learned from the super-popular/successful 6XX series + some innovations and created a model that truly "shines." And some of its flaws you forgive... They are expensive, yes, they are not the top, but they are among the best up to €1000, and think of it as getting 85% of the "audio nirvana," where for 100% you have to spend over €2000. And it is a model that will play perfectly for many years (I had the 580s until today from 1992!), constantly supported by the manufacturer, and upgraded *.
I wanted to write two things about these headphones, but I ended up going off track. Maybe because I'm listening to them now. I recommend them to you. And I believe you will get as excited as I am. I wish you happy listening!

(*) A decisive factor that made me "stay Sennheiser" is the incredible ease of finding and replacing all their components by the user without tools. In addition, all models in the 6XX series are fully compatible with each other. From headbands to drivers. Imagine, as soon as I got them, I put on the dt leather Dekoni earpads and the Cardas Clear cable that I had bought years ago from Drop for my 580s. Perfect fit. So you can upgrade them too! Keep that in mind. I should mention here for the skeptics that the above cable may give +40% to the overall performance. The Dekoni pads another 20%....