I dislike the Bluetooth because, according to my opinion are not so precise as the wired ones, since a loss of information is always possible.
It's "nice" to know when the audio is lossless but
you'd probably be surprised how good lossy compression can be in a
blind ABX test. (An ABX test is usually not practical with Bluetooth headphones because you' usually be listening to two different headphones which will sound different anyway.)
...An MP3 (lossy) can often sound identical to the uncompressed original in blind listening tests, or you may have to switch back-and-forth quickly and listen very carefully to hear a difference. Dolby on DVDs is also lossy compression and some of the best sounding music I have (IMO) is Dolby surround on concert DVDs. Some DVDs have a lossless stereo option but I always choose the surround and I don't notice any quality issues. (Most bad sound quality on DVDs is from old movies where the original quality wasn't that good.) ...Blu-Ray can have lossless surround.
I watched to the Beyerdinamics, but I don't know them.
If possible, it's helpful to go to an audio/video store to
listen for yourself. Opinions & preferences vary a lot! Even you don't buy from the store, or buy what they have to offer, it can be good to get an idea of what different headphones sound like. A long time ago I was thinking about upgrading my headphones but after going to the store I decided I liked what I already had better.
Of course, I am not able to pay 500 or 1000 $ to purchase a headset. Otherwise, there is no problem.
With headphones, there is almost no correlation between sound quality can price. You can sort the ASR headphone reviews by price or "recommended" and you'll see how random it is. The AKG K371 is highly rated for sound quality at about $150 USD. But it's closed-back and it seems to have a reputation of being "fragile". (I haven't broken mine but I don't listen to headphones that much.)
The main difference in sound quality and sound character is frequency response and frequency response can be tweaked with equalization, so
try some EQ before buying new headphones. If your source is a computer, software EQ is normally free!
The ASR headphones reviews all have recommended EQ settings or you can adjust to your own preference.
...There are limits with EQ and if you boost the bass too much you might push the headphone or amplifier into
distortion. Otherwise distortion from the headphones is rarely a problem. Amplifier distortion can be an issue from the headphone amp if you have to overdrive it to get the loudness you want.
With Bluetooth headphones you might some
noise (hiss). Passive headphones (no active electronics inside) don't generate noise, so any hiss & hum comes from the amplifier.
So with passive headphones
frequency response and distortion are the
ONLY sound-quality considerations.
Beware of headphone reviews where they use nonsense terminology to describe the sound! See
Audiophoolery.