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

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I have the 400s and the M20x BT variant, and the M20x is comfier on my above average sized head.
If you want REALLY big, Audio Technica ATH-M20XBT. No noise cancelling but great sound quality with wired and Bluetooth for $100-$150 (depending on sales). For noise cancelling, 1MORE Sonoflow SE is around $90-100 on Amazon. They're a slightly tighter fit than the ATHs, but they're still comfortable for my big head with glasses. I use them for 4-5+ hours at a time comfortably. The sound quality rivals my $400 ATH earbuds lol.
Audio Technica tend to lean more neutral but they're still good for all music types. The 1MORE headphones are probably heavier on the bass just because they're more isolated/closed. I wouldn't say either one are super bassy, but they're pretty well balanced. They're around $300 for the new model, but if you want BASS bass, check out the Skullcandy Crushers. They might be a bit tighter though, as a warning. Definitely look up reviews of these!
I have the budget model. Audio Technica ATH-M20x Bluetooth. Excellent over ear cans for the price.
So I have had a LOT of headphones over the years becuase I love trying them out. You are not going to get good NC for 60 quid, trust me. The best you could hope to find is a used pair of Momentum 4. I got mine for about that price, but I got lucky. I have those and the Sony WH1000XM5 or whatever they are called, and in all honesty, thanks to the software with a sensible EQ (the sony's have a shit EQ) they can sound quite good for the money. Want to buy new: My two cents; Forget about NC and get an AudioTechnica ATH-M20xbt. Don't expect too much from the microphone though.
I have two pairs of audio techica M20x BT one in black and one in white, I like them very much as they sit just right on my head to not be uncomfortable on top or on my ears. Battery life is stated to be 60H but I can go months without charging whilst using them daily on my commutes. Runs you about 70€, very bang for the buck imo.
Had the black m20’s for abt 2 years now and haven’t noticed any degradation in battery yet or any in the cushions, my wired m50x needs cushion replacements though but they are nearly 10y old at this point.
At least looking at the soundguys.com frequency response curves, the Sonoflow SE's seem to have less factory bass roll off than the ATH-M20XBT's, so if you want to just have good bass out of the box, then maybe go with the Sonoflow SE's. However, the ATH-M20XBT's have a similar bass roll off to my pair of Sennheiser HD 599 SE's, and I find these to have good bass for me after some EQ, so if you're fine with some EQ, you could pick up the ATH-M20XBT's if you prefer them. Honestly, assuming you just get a generally good pair of headphones with a fairly neutral sound profile, having good bass out of the box doesn't matter *that* much since you can always tweak the sound profile with an EQ.

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