
Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

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Yeah, I had the same thoughts. They are comfortable, well built, and sound like shit unless you’re looking for this very specific signature. If you want neutral/analytical, you’re better off with some BD’s and an EQ.
Finally someone else that doesn’t like the Meze sound. I wanted to like the 109 Pro so badly because it just looks so so good and feels great. But the sound profile is not for me at all. If you’re looking for some that fits between the HD600 and the Noire, the Focal Hadenys is worth a look - you can catch a deal on them if you’re patient and they are a good set. I also think that you will like the Arya Stealth if you get to try them. They were my endgame until one of the speakers died like a week after I got it. If you get one that works, they are an amazing daal.
The Meze 109 is a bright headphone with a strong bass presence and is not what I would consider a "natural sounding" headphone. For me it would be much closer to the HD660s2 than the 600 or 650. It is much better made than the Sennheiser headphones which are solid made but pretty much plastic all around. The wood earcups are a nice touch and the frame is manganese and not plastic. So clearly a premier looking open headphone. If you are interested in a closed headphone that is a bit more punchy than the HD600/650 the DCA Noire which comes with different pads to change tuning is one of my favorite headphones and the best closed headphone for me at that price. And really hard to compare to the 109 as the DCA is closed so starts a bit different. But of my closed headphones it isn't that far from the Meze 109 with a very solid bass and subtle V shaped sound presentation. To be clear, if you like the Meze 109 Pro (great headphone) with an AMP you are looking at \~$1000.
I got and returned the 109 Pro after few weeks. They are super comfortable, nice sounding and that is it. They are nice they didn't do much for me no complaints it just OK. I found my self going back more and more to my older Arya Stealth and 6xx. Obviously everyone is different but I think under $1000 there is much better at least objectively better headphones and you can listen to them first. Focal Clear, Arya Stealth, LCD-2C (used) I would even throw in 660S2. All these to me sounded better than 109 Pro.
ZMF Atrium for sure not even close. Own/Owned -> IE600, HD600, 6XX, Arya Stealth, Abyss Joal, LCD-2 Classic, Meze 109 Pro
Build quality is great. People hyped up the bass a lot and I found it disappointing. Overall the clarity/detail retrieval wasn't great either coming from the Arya stealth. I liked the 109 pro a lot more.
Got it. The best way to test that would be to see if there's a Hi-Fi or electronics shop near you that has any headphones you're interested in to demo. Actually, with a budget that high, plus the fact that you already own a Meze Boom mic, you could check out the 105 Silva or the 109 Pro. Those are also great headphones and would allow you to not buy a new mic.
Meze 109 Pro are the perfect balance of technical skill and musicality. Plus they are super comfortable and look like a piece of art.

Sennheiser
HD 560S
Budget gaming king with clear sound, but tight fit.

Sony
WH-1000XM4
ANC king, durable, but unreliable mic and touch controls.

Sennheiser
HD 6XX
Legendary mids, durable, but narrow soundstage and weak bass.

Sennheiser
HD 490 PRO
Super comfortable, wide soundstage for gaming, versatile pads.

Sennheiser
HD 599
Super comfortable, easy to drive, wide soundstage, open-back.

Ranked #1
Sennheiser - HD 6XX

Ranked #1
FiiO - FT1 Closed-back Headphones

Ranked #1
Sennheiser - HD 560S

Ranked #1
Sony - MDR-7506

Ranked #1
Sony - WH-1000XM4

Ranked #1
Sennheiser - HD 560S