Well, since I have the LCD3F as pretty much my favorite phone, my complementary phone presently is my Grado GS1000e. It is a more direct, live sound, with nice layering front to back and decent staging in other dimensions.
This Grado has images and vocals that are well defined in space, but of realistic (nicely large) size, with real meat-on-the-bones texture, natural texture. The bass is forceful and complete, but not overwhelming and flabby.
Yep, Grados are an acquired taste maybe, but the GS1Ke is for me, the best of Grado, the Grado for those have some issues with other Grados, like the RS and PS line (The PS pushes too powerfully for me often in the bass and sometimes in the highs, and makes my ears tired).
I had all three generations of the GS1000 over 5-6 years now, generally liked them all, and now like the e version a lot. It's a refined phone, natural, not over-the-top in the upper mids and highs, but very exciting.
So while my main go-to phone is the Audeze 3F, I use my GS1Ke almost as much. The e version adds some silk and liquidity to to vocals that is beguiling. No dryness at all. No sandpaper feeling whatsoever.
I like both these phones with tube and solid state amps, and they scale nicely.
I used to think the HD800 was the best complement, but there is still some raspiness and touches of high-frequency aggressiveness in vocals that is a problem for me, even though I still enjoy them. And somehow, relative to other phones, I keep feeling that the images should be bigger or closer. (This may just be my personal taste.) I call these non-fatal flaws.