I've been doing a little digging today myself, will keep an eye on Black Friday / Christmas deals coming up, and likely get a new set of headphones. The HD560S are popular, but shine for soundstage for movies, tv, and gaming (over music). They will still be really good for music, but the HD600/650 is definitely a step up when it comes to music (and a huge step up over your Audia Technica's). There is also a model named the Sennheiser HD6XX which is basically the same (or very similar) to the 650, but cheaper. I think this is the one I'll try to get. If using a pc, you will also want a DAC/AMP combo to get the full range of sound, and the best price on the market is probably the FiiO K11. An alternate is the Schiit Magni/Modi Stack (DAC and amp). Volcano can probably add more info and options to this. Keeping in mind I'm looking for ones that sound good for rock, if you want to crank "Everybody Dance Now" you may want more bass lol.
Generally speaking, based on my relatively limited knowledge, having the open back contributes to higher quality musical sound, especially for music and live albums. It may be that the one you tried earlier were not as good as a higher-end model, not sure. But I would say not to reject them entirely, without giving it one more chance. If you still don't like it you can always exchange or return it.
If however, you really only want a closed back, try AKG K371 or Beyerdynamic DT 700 Pro X.
And if you strongly insist on closed back Audio Technica, consider an upgrade to the ATH-M50x. It doesn't REQUIRE a DAC/amp, but will sound better with one.
I should add, I really prefer over-ear to on-ear. So it's possible the one you used was "on-ear" - over ears way more comfy imo.