If you have a bass problem you could find a filter of some kind that cuts the low bass. Some bass controls can do that. I haven’t found a music genre that totally lacks strong bass, although “acoustic” sometimes doesn’t have strong bass. Mainly, you should make sure your system is matched properly with amp and headphone, so the different frequencies are in balance. Then you will have better luck with different music.
Ok, it’s been a month and a lot of new experience. I’ve auditoned ATH M-50 (clamp’s too tight; they sweat my ears just from few minutes of exposure) and Senn HD 600 (the velour pad is amazingly comfortable & size is ok). So, long story short, now I can refine my search to: circumaural&non-pleather/foam pads, which brought me to Senn HD 439 (cloth) & 518 (velour).
I see, yes, but that should serve as an important lesson – the soundstage is not real in the same sense as actual tones, bass, treble, whatever. Soundstage is a perception that’s based on many factors, and here’s a challenge for you: You should be able to find some music tracks that have better soundstage on one headphone, and other tracks that will be better on the other headphone. Most of the time it will be just one way, but when a closed headphone beats an open headphone, I expect the open headphone will still show an advantage on some tracks. Your hearing perception could be tricked by simple things like a recess or emphasis in certain frequency ranges, or even phase shift when more than one driver is in the cup.
Although some headphones available are wired, many more are available that are wireless, and use Bluetooth to enable your music to be heard, even if the stereo or other device is several feet or even a few rooms away. Wired headphones deliver superior sound quality to wireless and Bluetooth because there's no chance of picking up interference from other devices, which sometimes happens with wireless headphones. In addition, wired headphones have no batteries to power them, so there's no chance of interruption should the batteries wear out.