So I've spent quite a few hours researching, reading and watching on headphones in general and especially all the recommendations. I've chosen the ones that seemed to have the best reviews in regards of my needs, one of which is competitive gaming. Here's my conclusion so far:
AKG K612 Pro:
Seemingly pretty much the only downside is that it doesn't do as well with fast-paced and energetic music (metal, hard rock in my case). Everything else, including detailed sounds, bass and competitive gaming seems quite perfect.
Beyerdynamic DT990 Pro:
Seems to provide very high level of comfort and an even higher level of sound quality than K612, however it's more bass-y (seemingly a bit 'too' bass-y in regards of the midrange), so it's harder to determine the positions in competitive gaming.
Seems to offer great sound quality (not as good as the other two, though), a bit less comfort, less immersive in games that do require immersion (story-driven) due to the mediocore bass, however they seem to be an excellent choice in regards of competitive gaming.
Superlux HD681 EVO:
Seems to provide decent sound quality and relatively okay level of comfort, however the sounds are not very detailed. That being said, as well as considering the general sound quality factor - the quality is moderately lower than that of the headphones above, especially the DT990. Considering that I'd buy the pads as well, it'd still be half the price of any other headphones listed.
To be honest, I mostly like DT990 and K612 - both the design and what they have to offer. HD598 is nice too in that sense, but somehow I like it less than the other two models, and Superlux seems like a great and much cheaper solution. K612 seems to have problems with detailed sounds and fast-paced/energetic music, while the DT990 seemingly puts too much emphasis on the bass which also screws up the mids a bit, whereas the HD598 puts too little emphasis on the bass, and Superlux seems to be of poorer quality overall (makes sense due to the price difference) than any of those, however it offers great quality for the price. I would say that the best choice would be K612 or DT990, but I'd like to receive some more feedback/advice on this, as it's hard for me to decide (and it's A LOT of money), even after spending hours researching about it - I have never researched into higher-level sound, and I understood little about Kave, except that it provided me with higher quality sound and had multiple speakers that gave me a very immersive feeling due to the positioning of sounds in games (5.1), as well as music that was blasting all over the cup rather than... Dryly, one-directional sound which was offered by every headphones I had prior to those.
Since all of them are open headphones, I wonder if I'd be able to hear my fans, people talking outside my room or kids playing outside (with my windows closed) - I can hear all of that without my headphones (my hearing's really good). Kave isolates it somewhat, I can still hear it, but not heavily at all, and for the most part a weak sound coming out of my headphones pretty much makes background noises unnoticeable (or close to that, if it's really weak). Sometimes I just wear it to cancel the background noises without anything playing (when I'm not gaming, the video card fan isn't that loud, so it reduces the general fan noise around by half, which is barely hearable. My phone says it's 10dB background fan noise under normal conditions, but I'd say it's around 20-25dB). When my VGA's fans are at the max (whenever I game), my phone says it goes up by ~10dB, but I think and a YouTube video says that it goes up to 60dB (say -10dB due to the PC case and distance, so 50dB where my ears are), and I can also hear the coil - I've a 7000s AMD card, which is a very annoying noise. I've looked into DT770s too, just in case - unfortunately it seems like they are pretty bad for competitive gaming, maybe not in itself, but in comparison to any of those. So basically I'm unsure as of how much of all of this I would be hearing - if I'd hear it just like it is, then I don't think I could ever get immersed into any game (as I'd be constantly hearing something outside of the game, play competitive games (I'd be hearing additional noises when I'd need silence to hear steps, etc.). I suppose I could crank up the volume when listening to music and watching movies - I do that anyway, but still - quiet scenes may not be as enjoyable if I could hear my fans more than I can hear them with my Kave. Gaming with Kave is alright too, it isn't that bad, except the static in the front speakers.