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

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Sennheiser Momentum 5. I have 4s which aren't as good but they were £120 off CEX. Sound quality is superb and I don't need noise cancelling. The 5's are better than your Sony xm's etc for noise cancelling plus superior sound.
For good sound quality, decent ANC, and without completely breaking your budget, the best option is by far the new Sennheiser Momentum 5. You will likely be able to find them on sale for that price, or on the used market by people regretting their impulse buy. They even have replaceable batteries, and Sennheiser headphones are known to be of high quality with good quality control, so they will likely last a very long time. Definitely your best choice.
Hahah thanks. Yeah, nowadays and the past year or so people rarely hand out those "!thanks". It was more a big thing a few years ago, so yeah 😅 The other suggestion from the other commenter is alright, but they are much more plastic-like and worse quality, and worse sound. If you want good quality, long lasting, great sound and decent ANC, then the Momentum 5 is probably your best option considering your budget, especially if you buy used, which I wouldn't worry about since they are new and it is Sennheiser.
You have some options although all wireless recommendations are to also get BTD700 dongle which will give you access to apt x adaptive which will help with low latency. The M4’s will be good in this use scenario (also the cheapest of the options given the M5 has just released). Next you have the M5 higher in cost due to just being released & the HDB630 which should come with the dongle. Overall given your lack of preference for audio quality the M4 plus dongle is best option. As for ANC like mentioned just have it in the middle of the slider (in the Smart Control plus app) which I believe is the off position.
I like the sound signature on Sennheiser Momentum Wireless. I have the latest version and it's definitely the best so far. But out of the box most don't sound that great for Deathcore, but an app like Wavelet will make a huge difference
Out of that lot I'd personally go for a Sennheiser Momentum wireless. I have a Hifiman HE400SE Which I love (I listen to mostly black and war metal generally, with some melo death occasionally) but they're open back planars so offer absolutely no noise isolation whatsoever, same goes for the majority of Hifiman headphones.
Sennheiser HD439 are the actual best sound quality, ohm resistance, build quality, weight, comfort quality, in relation to cost. I’ve done the research. I’ve also used the HD212s, HD280, Momentum Overears (I have two pairs of these, they’re the best all around headphones ever because of Bluetooth phone use). I have used HD600s as well, which obviously are amazing. But should only be used to mix songs professionally, what with the additional required amp to drive 300ohms

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