Well, you've discovered what many us here already knew. That's why you will many users here use the HD600/650 or 800. Others are Stax users, and Hifiman planars outnumber Audezes here by a wide margin. A lot of our discussion revolves around micro-details and 'plankton'.

It seems you will get along with a lot of us resolution whores here. So, welcome!

Mikoss did you try the mods that purrin posted in the other thread?

If I had LCD-3, they would have to be Don-modded.  I actually heard the LCD-3 almost too bright with his mods.  But if you have the LCD-3 sounding good in your system and nothing is missing, enjoy!  I went down the road of HDXX0 so didn't need to try that path but if you already have LCD-3 and want to see how far they can go (beyond the TP, etc.)...dBel had the knowledge.

What are your reference tracks for testing?

I tend to swear by the first minute of Dire Straits' "Money For Nothing" and the old James Brown & The JB's from the old mono days for quick listening tests. JB had one of the best sound guys in the music business.

You need a better amp for your LCD-3.  The Cavalli Liquid Carbon will likely do it and let you finally hear what the LCD-3 can do in comparison to the HD650/HD600.

I own a HD580 and HD600.  Both from about 15 years ago.  I also have an LCD-2r2 from Sept 2011 (it's all wood, no metal triangle cable mount thing).  My LCD-2r2 is probably on the veiled side compared to modern LCD-2.  I haven't done a lot of comparisons with other LCD-2 versions against my LCD-2.  I don't have access to enough other LCD-2's to really be doing that.

Even with my potentially (and likely) veiled LCD-2r2 I hear more micro-detail with it than my HD600 or HD580.  I also hear a more cohesive and deeper soundstage.  The trick is to use a very good amp for the LCD-2.  Use and amp that suits the LCD-2 well and you'll hear what it can do.  With the right amp the LCD-2 will shine.  The Audeze headphones need a good and synergistic amp to let them do the soundstage and micro-detail they are capable of.

I'm now using a Cavalli Liquid Fire because it suits the LCD-2 and other Audeze headphones so well.  The Liquid Fire gets the drivers to disappear.  It gets the headphones to sound like there are no drivers by my ears.  The drivers seem to disappear.  A lot of amps make the Audeze headphone sound like the drivers are right by my ears with the sound constrained by the ear cups and pumped at my ears.  The Cavalli lets the sound escape and sound free of the ear cups.  And the sound is able to be in front of my ear.  Centered at my temples or even out in front of my forehead.  Not many amps can do that.  The Cavalli can, and so can the Balancing Act, and a few others.  The amps that can do that are special.  This sort of sound though does depend on the quality of the recording.  Don't try to hear this with modern pop music. The HD600 also gets a lot of the same benefits when driven by the Liquid Fire.  Deep soundstage, ear cups disappear, etc.  It is a neat amp for that.  And demonstrates that the HD600 does scale with better amps.

I've also ordered a Liquid Carbon.  I haven't heard one yet.  Bought it just knowing it would be good.  I don't know how much of the Liquid Fire style deep soundstage it will do.  I suspect some.  Other Cavalli amps I've heard have some of that too.  It seems to be part of the Cavalli sound.  So wait till you get the Liquid Carbon.  You might find that the Audeze actually can do soundstage and not sound like drivers right next to your ears.

One test I use for detail is solo violin.  I have been using Hilary Hahn's recording of the Bach Partitas as a demo reference for a while.  So I've heard it with a variety of headphones and gear.  With the LCD-2, compared to the HD600, I hear more of the texture of the bow on the strings, more of the effect of the fingers on the strings, more of the notes bending due to the fingers hitting the strings and from vibrato.  I just hear more of what is being put in to the music.  I hear more of the performance.  The performance and the music is much more involving when listening to the LCD-2r2 compared to my HD600.  The tonality with the LCD-2 is off compared to the HD600.  There is no denying that.  The LCD-2 is not neutral.  But I'd much rather listen to that CD with my LCD-2 than my HD600.  The LCD-2 is just much more musical.  The trick though is to use a good amp.  With an average schitty amp I will EQ my LCD-2.  With a good amp like the Liquid Fire I don't feel the need to EQ it.

With a good amp and the LCD-2 I'm also able to hear the ambiance and space and the room in the recording.  The headphone is capable of letting you hear that.  And hear that better than I do w ith the HD600.  The trick is to use a good amp that synergizes with the Audeze headphones.  And Cavalli amps seem to hit that synergy.  My fingers are crossed that the Liquid Carbon will too.

I consider the HD600 to be my neutral reference.  But I listen mostly to my LCD-2r2 because it's musical and I hear more of the music and more of the recording with it than I do with the HD600.  To me my LCD-2r2 has much more micro-detail than my HD600 and better more cohesive soundstage too.  My LCD-2r2 has its faults.  But for now I can live with it since it does music in a way that can suit me.  I'm on the look for something better to me.