I love my HD6xx's. I've tried quite a few high-end headphones and I can say they all do something better. Some of them do everything better. Many of them are more exciting, have that "wow" factor. But the 600 series has this great, natural timbre where all of the music is. I also think people don't give them credit for how detailed they actually are. They do texture like almost nothing else. If I could find a pair of speakers with that fineness and ease to them, I'd be set. They do roll off in the highs and the sub bass. The 6xx have a bit of an upper mid dip that takes some bite from them. The upper treble and mid loss, you can somewhat EQ, but they get etchy. That is one thing about them. Not the 'clearest' in terms of background. It's not that you can't hear the background, but they can have a grain to them.
No amount of EQ will give you sub-bass. It has to do with the driver cage assembly and really just the smaller size of the driver. They aren't made for it in any capacity. Just past that is a midbass hump that people know as pillow bass. It has this fullness, but impact is vague. That can be corrected with damping. You can clean that up and get impact by removing the spider cage holding the driver magnet in and instead using sound dampener to hold the foam and magnet, while also helping to tame the bass ringing out. If you look at a CSD waterfall plot you can see where all of the bass distortion is. It hangs for quite a while, just resonating. Just don't cover the opening in the magnet. At that point you are doing surgery, though. You have to cut the spider cage off. Plenty of people do it. You can find the info out there.
To me, they kind of are what they are. I cycle headphones, but keep the HD6xx around as a headphone that I can use to enjoy any genre, whenever I feel like it. Through right place/right time I got myself a pretty nice SET tube amp made by a guy in Russia on a forum. He designed and built them himself, sold some made to order for a while. It has "robot_zombie" written on the back of it, hah. He sourced some killer transformers for it. Miles better amp than the ZDT Jr. or anything Woo Audio and I only spent around $300 for a hand-assembled brick of a tube amp. Transformers make or break those amps - much of what people associate with tube sound is likely due to transformers. Bad ones introduce things like bad stereo imaging, rolled off highs/lows, and just plain nasty distortion. "Intimate." "Syrupy." Good ones cost a pretty penny, as few make them in production quantities. I think this guy was able to get them because he was doing very small batches.
It does have quite a bit of 2nd order distortion to it. The hi-z output is 70 ohms, which ends up sounding niiicccee with the 650's. You wouldn't think it, but somehow that just brings them to life for me. That's a ~$500 setup that I can always keep around and use. Gotta be real deal tube amp though. I'm talking something with measurably high distortion. I think it really suits them. They do sound great on most sources these days, though. Even phones can drive them decently a lot of the time.
My throw in for bass planars is Audeze. Just my limited experience with bassy cans. I can at least speak for both the LCD-2 and Classic. Those have some serious chonk and thump to them. They also have some of the lowest distortion of pretty much any headphone across the entire bass region. Straight up just a flat line down there. And that EQs nicely. You can crank 40 or 60 hz on a wide Q and be swallowed by bass. Thing is, you have to be okay with the house sound. They have a weird recessed upper midrange that can make them a little laid back and do odd things to vocals. They are both very lively and dynamic but timbre suffers. I think they're great for any energetic electronic music. Lots of modern hip-hop for the same reason. Maybe rock and metal with some EQ. They can actually be great for that because in metal the guitars are often mixed atrociously - the timbre of the headphones brings more rhythmic cohesion. They're very 'quick' sounding. The attack on every instrument sounds like it breaks out of a singularity and just emerges there. I like my 2Cs for that sometimes. I feel and hear the drums and bass guitar in metal much more prominently.
They don't have fantastic imaging or staging. They are quite detailed, but it's not their strong suit. They do have big, tight, punchy bass. Every frequency responds well to EQ, you can make that work. I have the privilege of a hardware digital EQ with presets configured for genres, though. Still they're big, loud, built like tanks, and they hit. The LCD2's are the more balanced ones, which I would recommend to most people. 2c's only a certain kind of person can love. I would try before buying either. The tonality isn't an issue for a lot of people. If I need bass I will still put them on. It helps that they hold up well at high volume. I find that well-made planars generally don't "break away" as much in tone or overall placement of things in the mix as you increase the volume. They just sort of keep up. Audeze keep up so well you'll destroy your hearing before they're anywhere near breaking up.