@mRaaghavaI own both. Very different headphones. Both are excellent headphones, but they will not scratch the same itch. The XC has a good deal more speed and clarity, giving it a advantage in resolution and detail. The Atticus is much more analog sounding. The bass on the Atticus has bigger impact, more presence, and longer decay, but less extension into sub-bass. Overall, the tone is lusher and fuller, but more blurred together, especially in the mid range. The Atticus is a bit peakier in the treble, the XC has better presence past 10k. Both have pretty average soundstage. The XC has more precise and layered imaging, but the Atticus still does well with left/right positioning.
I have both headphones, too; however, my LCD-XC is the 2019 version, right before the (wood) cups were changed to its current incarnation.
My impressions of both headphones are similar to @phthora's. The LCD-XC has better balance and linearity in its sound. It eschews excessive bloom and warmth for a cleaner profile, with very good extension into the sub-bass region. There is adequate slam in the mid-bass, but its impact isn't quite as palpable as that on the Atticus. The LCD-XC is also a tad better resolving, but this can be easily ascribed to its leaner tone.
On the other hand, the Atticus is certainly warmer and fuller in its signature, offering a verdant, emotive experience. The lower register is a star performer on the Atticus, with tangible slam and presence. IMO, the Atticus is slightly more engaging, thanks to that grand mid-bass shelf.
Ultimately, if you're looking for a balanced sound with decent technicalities, go for the LCD-XC. If you want something that's more colored, with well-textured bass, try the Atticus.